Geometric And Spectral Analysis

Author : Pierre Albin,Dmitry Jakobson, Frédéric Rochon
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 48,9 Mb
Release : 2014-12-01
Category : Mathematics
ISBN : 9781470410438

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Geometric and Spectral Analysis by Pierre Albin,Dmitry Jakobson, Frédéric Rochon Pdf

In 2012, the Centre de Recherches Mathématiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants. This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4-8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2-6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23-27, 2012. The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kähler-Einstein metrics, analytic torsion, and Strichartz estimates. This book is co-published with the Centre de Recherches Mathématiques.

Author : Motoko Kotani, Hisashi Naito, T. Sunada, Tatsuya Tate
Publisher : American Mathematical Soc.
Page : 363 pages
File Size : 53,9 Mb
Release : 2009
Category : Number theory
ISBN : 9780821858127

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Spectral Analysis in Geometry and Number Theory by Motoko Kotani, Hisashi Naito, T. Sunada, Tatsuya Tate Pdf

Author : Jing Hua,Zichun Zhong
Publisher : Academic Press
Page : 152 pages
File Size : 50,6 Mb
Release : 2020-01-15
Category : Computers
ISBN : 9780128138427

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Spectral Geometry of Shapes by Jing Hua,Zichun Zhong Pdf

Spectral Geometry of Shapes presents unique shape analysis approaches based on shape spectrum in differential geometry. It provides insights on how to develop geometry-based methods for 3D shape analysis. The book is an ideal learning resource for graduate students and researchers in computer science, computer engineering and applied mathematics who have an interest in 3D shape analysis, shape motion analysis, image analysis, medical image analysis, computer vision and computer graphics. Due to the rapid advancement of 3D acquisition technologies there has been a big increase in 3D shape data that requires a variety of shape analysis methods, hence the need for this comprehensive resource. Presents the latest advances in spectral geometric processing for 3D shape analysis applications, such as shape classification, shape matching, medical imaging, etc. Provides intuitive links between fundamental geometric theories and real-world applications, thus bridging the gap between theory and practice Describes new theoretical breakthroughs in applying spectral methods for non-isometric motion analysis Gives insights for developing spectral geometry-based approaches for 3D shape analysis and deep learning of shape geometry

Author : Urakawa Hajime
Publisher : World Scientific
Page : 312 pages
File Size : 43,9 Mb
Release : 2017-06-02
Category : Mathematics
ISBN : 9789813109100

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Spectral Geometry Of The Laplacian: Spectral Analysis And Differential Geometry Of The Laplacian by Urakawa Hajime Pdf

The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian manifold. The continuity of the eigenvalue of the Laplacian, Cheeger and Yau's estimate of the first eigenvalue, the Lichnerowicz–Obata's theorem on the first eigenvalue, the Cheng's estimates of the kth eigenvalues, and Payne–Pólya–Weinberger's inequality of the Dirichlet eigenvalue of the Laplacian are also described. Then, the theorem of Colin de Verdière, that is, the spectrum determines the totality of all the lengths of closed geodesics is described. We give the V Guillemin and D Kazhdan's theorem which determines the Riemannian manifold of negative curvature.

Author : L. H. Koopmans
Publisher : Academic Press
Page : 383 pages
File Size : 51,5 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483218540

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The Spectral Analysis of Time Series by L. H. Koopmans Pdf

The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.

Author : Motoko Kotani,Hisashi Naito,Tatsuya Tate
Publisher : American Mathematical Soc.
Page : 363 pages
File Size : 44,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821842690

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Spectral Analysis in Geometry and Number Theory by Motoko Kotani,Hisashi Naito,Tatsuya Tate Pdf

This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007. Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.

Author : Klaus Kirsten
Publisher : Chapman and Hall/CRC
Page : 400 pages
File Size : 54,7 Mb
Release : 2001-12-13
Category : Science
ISBN : 158488259X

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Spectral Functions in Mathematics and Physics by Klaus Kirsten Pdf

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new, innovative methods for the exact analysis of a variety of spectral functions occurring in spectral geometry and under external conditions in statistical mechanics and quantum field theory. Spectral Functions in Mathematics and Physics presents a detailed overview of these advances. The author develops and applies methods for analyzing determinants arising when the external conditions originate from the Casimir effect, dielectric media, scalar backgrounds, and magnetic backgrounds. The zeta function underlies all of these techniques, and the book begins by deriving its basic properties and relations to the spectral functions. The author then uses those relations to develop and apply methods for calculating heat kernel coefficients, functional determinants, and Casimir energies. He also explores applications in the non-relativistic context, in particular applying the techniques to the Bose-Einstein condensation of an ideal Bose gas. Self-contained and clearly written, Spectral Functions in Mathematics and Physics offers a unique opportunity to acquire valuable new techniques, use them in a variety of applications, and be inspired to make further advances.

Author : Stefano Pigola,Marco Rigoli,Alberto G Setti
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 47,9 Mb
Release : 2008-05-28
Category : Mathematics
ISBN : 9783764386429

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Vanishing and Finiteness Results in Geometric Analysis by Stefano Pigola,Marco Rigoli,Alberto G Setti Pdf

This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.

Author : Mikhail Aleksandrovich Shubin,Maxim Braverman
Publisher : American Mathematical Soc.
Page : 223 pages
File Size : 48,8 Mb
Release : 2011-02-10
Category : Mathematics
ISBN : 9780821849484

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Spectral Theory and Geometric Analysis by Mikhail Aleksandrovich Shubin,Maxim Braverman Pdf

The papers in this volume cover important topics in spectral theory and geometric analysis such as resolutions of smooth group actions, spectral asymptotics, solutions of the Ginzburg-Landau equation, scattering theory, Riemann surfaces of infinite genus and tropical mathematics.

Author : Jaures Cecconi
Publisher : Unknown
Page : 262 pages
File Size : 54,9 Mb
Release : 2011-03-30
Category : Electronic
ISBN : 364210956X

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Spectral Analysis by Jaures Cecconi Pdf

Author : Jaures Cecconi
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 46,7 Mb
Release : 2011-06-04
Category : Mathematics
ISBN : 9783642109553

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Spectral Analysis by Jaures Cecconi Pdf

G. Bottaro: Quelques résultats d’analyse spectrale pour des opérateurs différentiels à coefficients constants sur des domaines non bornés.- L. Gårding: Eigenfuction expansions.- C. Goulaouic: Valeurs propres de problèmes aux limites irréguliers: applications.- G. Grubb: Essential spectra of elliptic systems on compact manifolds.- J.Cl. Guillot: Quelques résultats récents en Scattering.- N. Schechter: Theory of perturbations of partial differential operators.- C.H. Wilcox: Spectral analysis of the Laplacian with a discontinuous coefficient.

Author : R. B. Holmes
Publisher : Springer
Page : 0 pages
File Size : 45,9 Mb
Release : 2012-12-12
Category : Mathematics
ISBN : 146849371X

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Geometric Functional Analysis and its Applications by R. B. Holmes Pdf

This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its appli cations. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the Hahn Banach principle, the latter appearing in ten different but equivalent formula tions (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces.

Author : Alexandre Girouard
Publisher : Unknown
Page : 298 pages
File Size : 54,8 Mb
Release : 2017
Category : Geometry, Differential
ISBN : 1470442582

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Geometric and Computational Spectral Theory by Alexandre Girouard Pdf

The book is a collection of lecture notes and survey papers based on the mini-courses given by leading experts at the 2015 Séminaire de Mathématiques Supérieures on Geometric and Computational Spectral Theory, held from June 15-26, 2015, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The volume covers a broad variety of topics in spectral theory, highlighting its connections to differential geometry, mathematical physics and numerical analysis, bringing together the theoretical and computational approaches to spectral theory, and emphasizing the interplay between the two.

Author : Lambert H. Koopmans
Publisher : Elsevier
Page : 385 pages
File Size : 55,5 Mb
Release : 1995-05-18
Category : Mathematics
ISBN : 9780080541563

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The Spectral Analysis of Time Series by Lambert H. Koopmans Pdf

To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results.The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications.Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction. Hilbert spaces univariate models for spectral analysis multivariate spectral models sampling, aliasing, and discrete-time models real-time filtering digital filters linear filters distribution theory sampling properties of spectral estimates linear prediction

Author : Pierre H. Berard
Publisher : Springer
Page : 284 pages
File Size : 41,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540409588

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Spectral Geometry by Pierre H. Berard Pdf