Geometric And Spectral Analysis

Author : Pierre Albin
Publisher : American Mathematical Soc.
ISBN 13 : 1470410435
Total Pages : 378 pages
Book Rating : 4.38/5 ( download)

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Download or read book Geometric and Spectral Analysis written by Pierre Albin and published by American Mathematical Soc.. This book was released on 2014-12-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jing Hua
Publisher : Academic Press
ISBN 13 : 0128138424
Total Pages : 152 pages
Book Rating : 4.27/5 ( download)

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Download or read book Spectral Geometry of Shapes written by Jing Hua and published by Academic Press. This book was released on 2020-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : L. H. Koopmans
Publisher : Academic Press
ISBN 13 : 1483218546
Total Pages : 383 pages
Book Rating : 4.40/5 ( download)

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Download or read book The Spectral Analysis of Time Series written by L. H. Koopmans and published by Academic Press. This book was released on 2014-05-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : American Mathematical Soc.
ISBN 13 : 0821842692
Total Pages : 363 pages
Book Rating : 4.90/5 ( download)

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Download or read book Spectral Analysis in Geometry and Number Theory written by Motoko Kotani and published by American Mathematical Soc.. This book was released on 2009 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Motoko Kotani, Hisashi Naito, T. Sunada, Tatsuya Tate
Publisher : American Mathematical Soc.
ISBN 13 : 0821858122
Total Pages : 363 pages
Book Rating : 4.27/5 ( download)

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Download or read book Spectral Analysis in Geometry and Number Theory written by Motoko Kotani, Hisashi Naito, T. Sunada, Tatsuya Tate and published by American Mathematical Soc.. This book was released on 2009 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Urakawa Hajime
Publisher : World Scientific
ISBN 13 : 9813109106
Total Pages : 312 pages
Book Rating : 4.00/5 ( download)

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Download or read book Spectral Geometry Of The Laplacian: Spectral Analysis And Differential Geometry Of The Laplacian written by Urakawa Hajime and published by World Scientific. This book was released on 2017-06-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : R. B. Holmes
Publisher : Springer
ISBN 13 : 9781468493719
Total Pages : 0 pages
Book Rating : 4.1X/5 ( download)

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Download or read book Geometric Functional Analysis and its Applications written by R. B. Holmes and published by Springer. This book was released on 2012-12-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Pierre H. Berard
Publisher : Springer
ISBN 13 : 3540409580
Total Pages : 284 pages
Book Rating : 4.88/5 ( download)

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Download or read book Spectral Geometry written by Pierre H. Berard and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Stefano Pigola
Publisher : Springer Science & Business Media
ISBN 13 : 3764386428
Total Pages : 282 pages
Book Rating : 4.29/5 ( download)

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Download or read book Vanishing and Finiteness Results in Geometric Analysis written by Stefano Pigola and published by Springer Science & Business Media. This book was released on 2008-05-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bo'az Klartag
Publisher : Springer
ISBN 13 : 3319094777
Total Pages : 459 pages
Book Rating : 4.79/5 ( download)

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Download or read book Geometric Aspects of Functional Analysis written by Bo'az Klartag and published by Springer. This book was released on 2014-10-08 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis. Most of the papers deal with different aspects of Asymptotic Geometric Analysis, understood in a broad sense; many continue the study of geometric and volumetric properties of convex bodies and log-concave measures in high-dimensions and in particular the mean-norm, mean-width, metric entropy, spectral-gap, thin-shell and slicing parameters, with applications to Dvoretzky and Central-Limit-type results. The study of spectral properties of various systems, matrices, operators and potentials is another central theme in this volume. As expected, probabilistic tools play a significant role and probabilistic questions regarding Gaussian noise stability, the Gaussian Free Field and First Passage Percolation are also addressed. The historical connection to the field of Classical Convexity is also well represented with new properties and applications of mixed-volumes. The interplay between the real convex and complex pluri-subharmonic settings continues to manifest itself in several additional articles. All contributions are original research papers and were subject to the usual refereeing standards.