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The Resource Fractal Zeta Functions and Fractal Drums : Higher-Dimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource)

Fractal Zeta Functions and Fractal Drums : Higher-Dimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource)

Label
Fractal Zeta Functions and Fractal Drums : Higher-Dimensional Theory of Complex Dimensions
Title
Fractal Zeta Functions and Fractal Drums
Title remainder
Higher-Dimensional Theory of Complex Dimensions
Statement of responsibility
by Michel L. Lapidus, Goran Radunović, Darko Žubrinić
Creator
Contributor
Author
Subject
Language
eng
Summary
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional 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 step-by-step 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.--
Member of
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 : Higher-Dimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-44706-3
Instantiates
Publication
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 Dirchlet-Type 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
978-3-319-44706-3
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, non-commercial 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
10.1007/978-3-319-44706-3
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 : Higher-Dimensional Theory of Complex Dimensions, by Michel L. Lapidus, Goran Radunović, Darko Žubrinić, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-44706-3
Publication
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 Dirchlet-Type 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
978-3-319-44706-3
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, non-commercial 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
10.1007/978-3-319-44706-3
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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