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The Resource Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings, by Michel L. Lapidus, Machiel van Frankenhuijsen, (electronic resource)
Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings, by Michel L. Lapidus, Machiel van Frankenhuijsen, (electronic resource)
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The item Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings, by Michel L. Lapidus, Machiel van Frankenhuijsen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
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The item Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings, by Michel L. Lapidus, Machiel van Frankenhuijsen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary

 Number theory, spectral geometry, and fractal geometry are interlinked in this indepth study of the vibrations of fractal strings; that is, onedimensional drums with fractal boundary. This second edition of Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical physics. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented
 ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results
 Language
 eng
 Edition
 2nd ed. 2013.
 Extent
 XXVI, 567 p. 73 illus.
 Contents

 Preface
 Overview
 Introduction
 1. Complex Dimensions of Ordinary Fractal Strings
 2. Complex Dimensions of SelfSimilar Fractal Strings
 3. Complex Dimensions of Nonlattice SelfSimilar Strings
 4. Generalized Fractal Strings Viewed as Measures
 5. Explicit Formulas for Generalized Fractal Strings
 6. The Geometry and the Spectrum of Fractal Strings
 7. Periodic Orbits of SelfSimilar Flows
 8. Fractal Tube Formulas
 9. Riemann Hypothesis and Inverse Spectral Problems
 10. Generalized Cantor Strings and their Oscillations
 11. Critical Zero of Zeta Functions
 12 Fractality and Complex Dimensions
 13. Recent Results and Perspectives
 Appendix A. Zeta Functions in Number Theory
 Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics
 Appendix C. An Application of Nevanlinna Theory
 Bibliography
 Author Index
 Subject Index
 Index of Symbols
 Conventions
 Acknowledgements
 Isbn
 9781461421764
 Label
 Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings
 Title
 Fractal Geometry, Complex Dimensions and Zeta Functions
 Title remainder
 Geometry and Spectra of Fractal Strings
 Statement of responsibility
 by Michel L. Lapidus, Machiel van Frankenhuijsen
 Subject

 Differential equations, partial
 Differential equations, partial
 Differential equations, partial
 Dynamical Systems and Ergodic Theory
 Electronic resources
 Functional Analysis
 Functional Analysis
 Functional Analysis
 Functional analysis
 Functional analysis
 Functional analysis
 Global Analysis and Analysis on Manifolds
 Global analysis
 Mathematics
 Mathematics
 Mathematics
 Measure and Integration
 Number Theory
 Number Theory
 Number Theory
 Number theory
 Number theory
 Number theory
 Partial Differential Equations
 Differentiable dynamical systems
 Differentiable dynamical systems
 Differentiable dynamical systems
 Language
 eng
 Summary

 Number theory, spectral geometry, and fractal geometry are interlinked in this indepth study of the vibrations of fractal strings; that is, onedimensional drums with fractal boundary. This second edition of Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical physics. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented
 ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of numbertheoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: " The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." —NicolaeAdrian Secelean, Zentralblatt Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for selfsimilar flows, and a geometric tube formula · The method of Diophantine approximation is used to study selfsimilar strings and flows · Analytical and geometric methods are used to obtain new results
 http://library.link/vocab/creatorName
 Lapidus, Michel L
 Image bit depth
 0
 LC call number
 QA241247.5
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 van Frankenhuijsen, Machiel.
 SpringerLink
 Series statement
 Springer Monographs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Differentiable dynamical systems
 Functional analysis
 Global analysis
 Differential equations, partial
 Number theory
 Mathematics
 Number Theory
 Measure and Integration
 Partial Differential Equations
 Dynamical Systems and Ergodic Theory
 Global Analysis and Analysis on Manifolds
 Functional Analysis
 Label
 Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings, by Michel L. Lapidus, Machiel van Frankenhuijsen, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  Overview  Introduction  1. Complex Dimensions of Ordinary Fractal Strings  2. Complex Dimensions of SelfSimilar Fractal Strings  3. Complex Dimensions of Nonlattice SelfSimilar Strings  4. Generalized Fractal Strings Viewed as Measures  5. Explicit Formulas for Generalized Fractal Strings  6. The Geometry and the Spectrum of Fractal Strings  7. Periodic Orbits of SelfSimilar Flows  8. Fractal Tube Formulas  9. Riemann Hypothesis and Inverse Spectral Problems  10. Generalized Cantor Strings and their Oscillations  11. Critical Zero of Zeta Functions  12 Fractality and Complex Dimensions  13. Recent Results and Perspectives  Appendix A. Zeta Functions in Number Theory  Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics  Appendix C. An Application of Nevanlinna Theory  Bibliography  Author Index  Subject Index  Index of Symbols  Conventions  Acknowledgements
 Dimensions
 unknown
 Edition
 2nd ed. 2013.
 Extent
 XXVI, 567 p. 73 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9781461421764
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781461421764
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9781461421764
 Label
 Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings, by Michel L. Lapidus, Machiel van Frankenhuijsen, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  Overview  Introduction  1. Complex Dimensions of Ordinary Fractal Strings  2. Complex Dimensions of SelfSimilar Fractal Strings  3. Complex Dimensions of Nonlattice SelfSimilar Strings  4. Generalized Fractal Strings Viewed as Measures  5. Explicit Formulas for Generalized Fractal Strings  6. The Geometry and the Spectrum of Fractal Strings  7. Periodic Orbits of SelfSimilar Flows  8. Fractal Tube Formulas  9. Riemann Hypothesis and Inverse Spectral Problems  10. Generalized Cantor Strings and their Oscillations  11. Critical Zero of Zeta Functions  12 Fractality and Complex Dimensions  13. Recent Results and Perspectives  Appendix A. Zeta Functions in Number Theory  Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics  Appendix C. An Application of Nevanlinna Theory  Bibliography  Author Index  Subject Index  Index of Symbols  Conventions  Acknowledgements
 Dimensions
 unknown
 Edition
 2nd ed. 2013.
 Extent
 XXVI, 567 p. 73 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9781461421764
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781461421764
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9781461421764
Subject
 Differential equations, partial
 Differential equations, partial
 Differential equations, partial
 Dynamical Systems and Ergodic Theory
 Electronic resources
 Functional Analysis
 Functional Analysis
 Functional Analysis
 Functional analysis
 Functional analysis
 Functional analysis
 Global Analysis and Analysis on Manifolds
 Global analysis
 Mathematics
 Mathematics
 Mathematics
 Measure and Integration
 Number Theory
 Number Theory
 Number Theory
 Number theory
 Number theory
 Number theory
 Partial Differential Equations
 Differentiable dynamical systems
 Differentiable dynamical systems
 Differentiable dynamical systems
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