The Resource Fractal Zeta Functions and Fractal Drums : HigherDimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource)
Fractal Zeta Functions and Fractal Drums : HigherDimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource)
Resource Information
The item Fractal Zeta Functions and Fractal Drums : HigherDimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Fractal Zeta Functions and Fractal Drums : HigherDimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This monograph gives a stateoftheart and accessible treatment of a new general higherdimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed stepbystep at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the first time that essential singularities of fractal zeta functions can naturally emerge for various classes of fractal sets and have a significant geometric effect. The theory developed in this book leads naturally to a new definition of fractality, expressed in terms of the existence of underlying geometric oscillations or, equivalently, in terms of the existence of nonreal complex dimensions. The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field.
 Language
 eng
 Extent
 1 online resource (XL, 655 pages)
 Contents

 Overview
 Preface
 List of Figures
 Key Words
 Selected Key Results
 Glossary
 1. Introduction
 2 Distance and Tube Zeta Functions
 3. Applications of Distance and Tube Zeta Functions
 4. Relative Fractal Drums and Their Complex Dimensions
 5.Fractal Tube Formulas and Complex Dimensions
 6. Classification of Fractal Sets and Concluding Comments
 Appendix A. Tame DirchletType Integrals
 Appendix B. Local Distance Zeta Functions
 Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs
 Acknowledgements
 Bibliography
 Author Index
 Subject Index.
 Isbn
 9783319447063
 Label
 Fractal Zeta Functions and Fractal Drums : HigherDimensional Theory of Complex Dimensions
 Title
 Fractal Zeta Functions and Fractal Drums
 Title remainder
 HigherDimensional Theory of Complex Dimensions
 Statement of responsibility
 by Michel L. Lapidus, Goran Radunović, Darko Žubrinić
 Language
 eng
 Summary
 This monograph gives a stateoftheart and accessible treatment of a new general higherdimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed stepbystep at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the first time that essential singularities of fractal zeta functions can naturally emerge for various classes of fractal sets and have a significant geometric effect. The theory developed in this book leads naturally to a new definition of fractality, expressed in terms of the existence of underlying geometric oscillations or, equivalently, in terms of the existence of nonreal complex dimensions. The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Lapidus, Michel L
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName

 Radunović, Goran.
 Žubrinić, Darko.
 Series statement

 Springer eBooks
 Springer Monographs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Measure theory
 Number theory
 Mathematical physics
 Label
 Fractal Zeta Functions and Fractal Drums : HigherDimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (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
 Overview  Preface  List of Figures  Key Words  Selected Key Results  Glossary  1. Introduction  2 Distance and Tube Zeta Functions  3. Applications of Distance and Tube Zeta Functions  4. Relative Fractal Drums and Their Complex Dimensions  5.Fractal Tube Formulas and Complex Dimensions  6. Classification of Fractal Sets and Concluding Comments  Appendix A. Tame DirchletType Integrals  Appendix B. Local Distance Zeta Functions  Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs  Acknowledgements  Bibliography  Author Index  Subject Index.
 Control code
 9783319447063
 Dimensions
 unknown
 Extent
 1 online resource (XL, 655 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319447063
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319447063
 Other physical details
 55 illustrations, 10 illustrations in color.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)990265562
 Label
 Fractal Zeta Functions and Fractal Drums : HigherDimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (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
 Overview  Preface  List of Figures  Key Words  Selected Key Results  Glossary  1. Introduction  2 Distance and Tube Zeta Functions  3. Applications of Distance and Tube Zeta Functions  4. Relative Fractal Drums and Their Complex Dimensions  5.Fractal Tube Formulas and Complex Dimensions  6. Classification of Fractal Sets and Concluding Comments  Appendix A. Tame DirchletType Integrals  Appendix B. Local Distance Zeta Functions  Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs  Acknowledgements  Bibliography  Author Index  Subject Index.
 Control code
 9783319447063
 Dimensions
 unknown
 Extent
 1 online resource (XL, 655 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319447063
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319447063
 Other physical details
 55 illustrations, 10 illustrations in color.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)990265562
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/FractalZetaFunctionsandFractalDrums/7PUrLD25ViI/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/FractalZetaFunctionsandFractalDrums/7PUrLD25ViI/">Fractal Zeta Functions and Fractal Drums : HigherDimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>