Progress In Inverse Spectral Geometry

Author : Stig I. Andersson,Michel L. Lapidus
Publisher : Birkhäuser
Page : 202 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889384

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Progress in Inverse Spectral Geometry by Stig I. Andersson,Michel L. Lapidus Pdf

Most polynomial growth on every half-space Re (z) ::::: c. Moreover, Op(t) depends holomorphically on t for Re t> O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are [A-P-S] and [Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e- ; namely, u(·, t) = V(t)uoU· Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt, E* ®E), locally given by 00 K(x, y; t) = L>-IAk(~k ® 'Pk)(X, y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2::>- k. k=O Now, using, e. g., the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op.

Author : Stig I Andersson,Michel Lapidus
Publisher : Unknown
Page : 212 pages
File Size : 40,7 Mb
Release : 1997-10-01
Category : Electronic
ISBN : 3034889399

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Progress in Inverse Spectral Geometry by Stig I Andersson,Michel Lapidus Pdf

Author : Stig Ingvar Andersson,Michel Laurent Lapidus
Publisher : Unknown
Page : 196 pages
File Size : 47,8 Mb
Release : 1997
Category : Inverse problems (Differential equations)
ISBN : 081765755X

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Progress in Inverse Spectral Geometry by Stig Ingvar Andersson,Michel Laurent Lapidus Pdf

Author : Stig I. Andersson,Michel Lapidus
Publisher : Birkhäuser
Page : 197 pages
File Size : 48,5 Mb
Release : 2012-10-12
Category : Mathematics
ISBN : 3034898355

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Progress in Inverse Spectral Geometry by Stig I. Andersson,Michel Lapidus Pdf

most polynomial growth on every half-space Re (z) ::::: c. Moreover, Op(t) depends holomorphically on t for Re t > O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are [A-P-S] and [Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x,O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e- ; namely, u(·, t) = V(t)uoU· Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt,E* ®E), locally given by 00 K(x,y; t) = L>-IAk(~k ® 'Pk)(X,y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2::>- k. k=O Now, using, e. g. , the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op.

Author : Pierre H. Berard
Publisher : Springer
Page : 284 pages
File Size : 43,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540409588

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Spectral Geometry by Pierre H. Berard Pdf

Author : M.-E. Craioveanu,Mircea Puta,Themistocles RASSIAS
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 43,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401724753

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Old and New Aspects in Spectral Geometry by M.-E. Craioveanu,Mircea Puta,Themistocles RASSIAS Pdf

It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively. If M is closed, the spectrum of each such operator is an infinite divergent sequence of real numbers, each eigenvalue being repeated according to its finite multiplicity. Spectral Geometry is concerned with the spectra of these operators, also the extent to which these spectra determine the geometry of (M, g) and the topology of M. This problem has been translated by several authors (most notably M. Kac). into the col loquial question "Can one hear the shape of a manifold?" because of its analogy with the wave equation. This terminology was inspired from earlier results of H. Weyl. It is known that the above spectra cannot completely determine either the geometry of (M , g) or the topology of M. For instance, there are examples of pairs of closed Riemannian manifolds with the same spectra corresponding to the Laplace-Beltrami operators, but which differ substantially in their geometry and which are even not homotopically equiva lent.

Author : Anonim
Publisher : Unknown
Page : 271 pages
File Size : 50,5 Mb
Release : 1969
Category : Eigenvalues
ISBN : 8524400277

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Monografias de matemática by Anonim Pdf

Author : Alex Barnett
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 41,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853191

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Spectral Geometry by Alex Barnett Pdf

This volume contains the proceedings of the International Conference on Spectral Geometry, held July 19-23, 2010, at Dartmouth College, Dartmouth, New Hampshire. Eigenvalue problems involving the Laplace operator on manifolds have proven to be a consistently fertile area of geometric analysis with deep connections to number theory, physics, and applied mathematics. Key questions include the measures to which eigenfunctions of the Laplacian on a Riemannian manifold condense in the limit of large eigenvalue, and the extent to which the eigenvalues and eigenfunctions of a manifold encode its geometry. In this volume, research and expository articles, including those of the plenary speakers Peter Sarnak and Victor Guillemin, address the flurry of recent progress in such areas as quantum unique ergodicity, isospectrality, semiclassical measures, the geometry of nodal lines of eigenfunctions, methods of numerical computation, and spectra of quantum graphs. This volume also contains mini-courses on spectral theory for hyperbolic surfaces, semiclassical analysis, and orbifold spectral geometry that prepared the participants, especially graduate students and young researchers, for conference lectures.

Author : Chrisopher B. Croke,Gunther Uhlmann,Irena Lasiecka,Michael Vogelius
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493757

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Geometric Methods in Inverse Problems and PDE Control by Chrisopher B. Croke,Gunther Uhlmann,Irena Lasiecka,Michael Vogelius Pdf

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.

Author : Lino Di Martino,William Kantor,Guglielmo Lunardon,Antonio Pasini,Maria Clara Tamburini
Publisher : Birkhäuser
Page : 267 pages
File Size : 42,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783034888196

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Groups and Geometries by Lino Di Martino,William Kantor,Guglielmo Lunardon,Antonio Pasini,Maria Clara Tamburini Pdf

On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of finite characteristic, 3. buildings, and the geometry of projective and polar spaces, and 4. geometries of sporadic simple groups. We are grateful to the authors for their efforts in providing us with manuscripts in LaTeX. Barbara Priwitzer and Thomas Hintermann, Mathematics Editors of Birkhauser, have been very helpful and supportive throughout the preparation of this volume.

Author : Robert Brooks,Michael Entov,Yehuda Pinchover,Michah Sageev
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 48,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837108

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Geometry, Spectral Theory, Groups, and Dynamics by Robert Brooks,Michael Entov,Yehuda Pinchover,Michah Sageev Pdf

This volume contains articles based on talks given at the Robert Brooks Memorial Conference on Geometry and Spectral Theory and the Workshop on Groups, Geometry and Dynamics held at Technion - the Israel Institute of Technology (Haifa). Robert Brooks' (1952-2002) broad range of mathematical interests is represented in the volume, which is devoted to various aspects of global analysis, spectral theory, the theory of Riemann surfaces, Riemannian and discrete geometry, and number theory. A survey of Brooks' work has been written by his close colleague, Peter Buser. Also included in the volume are articles on analytic topics, such as Szegos theorem, and on geometric topics, such as isoperimetric inequalities and symmetries of manifolds. The book is suitable for graduate students and researchers interested in various aspects of geometry and global analysis.

Author : Donatella Danielli,Irina Mitrea
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 41,8 Mb
Release : 2020-04-09
Category : Education
ISBN : 9781470448967

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Advances in Harmonic Analysis and Partial Differential Equations by Donatella Danielli,Irina Mitrea Pdf

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Partial Differential Equations, held from April 21–22, 2018, at Northeastern University, Boston, Massachusetts. The book features a series of recent developments at the interface between harmonic analysis and partial differential equations and is aimed toward the theoretical and applied communities of researchers working in real, complex, and harmonic analysis, partial differential equations, and their applications. The topics covered belong to the general areas of the theory of function spaces, partial differential equations of elliptic, parabolic, and dissipative types, geometric optics, free boundary problems, and ergodic theory, and the emphasis is on a host of new concepts, methods, and results.

Author : Marcel Berger
Publisher : Springer Science & Business Media
Page : 852 pages
File Size : 50,9 Mb
Release : 2007-06-29
Category : Mathematics
ISBN : 3540653171

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A Panoramic View of Riemannian Geometry by Marcel Berger Pdf

This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS

Author : Ricardo Baeza-Yates,Joseph Glaz,Henryk Gzyl,Jürg Hüsler,José Luis Palacios
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 48,5 Mb
Release : 2006-02-28
Category : Mathematics
ISBN : 9780387233949

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Recent Advances in Applied Probability by Ricardo Baeza-Yates,Joseph Glaz,Henryk Gzyl,Jürg Hüsler,José Luis Palacios Pdf

Applied probability is a broad research area that is of interest to scientists in diverse disciplines in science and technology, including: anthropology, biology, communication theory, economics, epidemiology, finance, geography, linguistics, medicine, meteorology, operations research, psychology, quality control, sociology, and statistics. Recent Advances in Applied Probability is a collection of survey articles that bring together the work of leading researchers in applied probability to present current research advances in this important area. This volume will be of interest to graduate students and researchers whose research is closely connected to probability modelling and their applications. It is suitable for one semester graduate level research seminar in applied probability.

Author : S.K. Jain,Rizvi S. Tariq
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461219781

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Advances in Ring Theory by S.K. Jain,Rizvi S. Tariq Pdf