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05244nam a22005895i 4500 |
| 001 - CONTROL NUMBER |
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978-0-387-35208-4 |
| 003 - CONTROL NUMBER IDENTIFIER |
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DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20161121231026.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
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100301s2006 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780387352084 |
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978-0-387-35208-4 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-0-387-35208-4 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA611-614.97 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBP |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT038000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
514 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Lapidus, Michel L. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Fractal Geometry, Complex Dimensions and Zeta Functions |
| Medium |
[electronic resource] : |
| Remainder of title |
Geometry and Spectra of Fractal Strings / |
| Statement of responsibility, etc. |
by Michel L. Lapidus, Machiel van Frankenhuijsen. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
New York, NY : |
| Name of producer, publisher, distributor, manufacturer |
Springer New York, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2006. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XXIV, 460 p. 54 illus. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Springer Monographs in Mathematics, |
| International Standard Serial Number |
1439-7382 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Complex Dimensions of Ordinary Fractal Strings -- Complex Dimensions of Self-Similar Fractal Strings -- Complex Dimensions of Nonlattice Self-Similar Strings: Quasiperiodic Patterns and Diophantine Approximation -- Generalized Fractal Strings Viewed as Measures -- Explicit Formulas for Generalized Fractal Strings -- The Geometry and the Spectrum of Fractal Strings -- Periodic Orbits of Self-Similar Flows -- Tubular Neighborhoods and Minkowski Measurability -- The Riemann Hypothesis and Inverse Spectral Problems -- Generalized Cantor Strings and their Oscillations -- The Critical Zeros of Zeta Functions -- Concluding Comments, Open Problems, and Perspectives. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Key Features The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then 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 self-similar flows, and a geometric tube formula The method of Diophantine approximation is used to study self-similar strings and flows Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts, and discusses several open problems and extensions. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics. From Reviews of Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, by Michel Lapidus and Machiel van Frankenhuysen, Birkhäuser Boston Inc., 2000. "This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style." –Mathematical Reviews "It is the reviewer’s opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced." –Bulletin of the London Mathematical Society. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Dynamics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Ergodic theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Global analysis (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Manifolds (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Measure theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Partial differential equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Number theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Topology. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Topology. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Number Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Measure and Integration. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Partial Differential Equations. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Dynamical Systems and Ergodic Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Global Analysis and Analysis on Manifolds. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Frankenhuijsen, Machiel van. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9780387332857 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Springer Monographs in Mathematics, |
| International Standard Serial Number |
1439-7382 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-0-387-35208-4 |
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ZDB-2-SMA |
