Spectral Geometry Of Partial Differential Operators
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Author | : Michael Ruzhansky |
Publisher | : CRC Press |
Total Pages | : 366 |
Release | : 2020-02-07 |
Genre | : Mathematics |
ISBN | : 0429780575 |
Download Spectral Geometry of Partial Differential Operators Book in PDF, Epub and Kindle
The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations. Historically, one of the first inequalities of the spectral geometry was the minimization problem of the first eigenvalue of the Dirichlet Laplacian. Nowadays, this type of inequalities of spectral geometry have expanded to many other cases with number of applications in physics and other sciences. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of (partial differential) operators on arbitrary domains. Features: Collects the ideas underpinning the inequalities of the spectral geometry, in both self-adjoint and non-self-adjoint operator theory, in a way accessible by anyone with a basic level of understanding of linear differential operators Aimed at theoretical as well as applied mathematicians, from a wide range of scientific fields, including acoustics, astronomy, MEMS, and other physical sciences Provides a step-by-step guide to the techniques of non-self-adjoint partial differential operators, and for the applications of such methods. Provides a self-contained coverage of the traditional and modern theories of linear partial differential operators, and does not require a previous background in operator theory.
Author | : Pierre H. Berard |
Publisher | : Springer |
Total Pages | : 284 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540409580 |
Download Spectral Geometry Book in PDF, Epub and Kindle
Author | : |
Publisher | : |
Total Pages | : 0 |
Release | : 2020 |
Genre | : |
ISBN | : |
Download Spectral Geometry of Partial Differential Operators Book in PDF, Epub and Kindle
Access; Differential; Durvudkhan; Geometry; Makhmud; Michael; OA; Open; Operators; Partial; Ruzhansky; Sadybekov; Spectral; Suragan.
Author | : Gerd Grubb |
Publisher | : American Mathematical Soc. |
Total Pages | : 338 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 082183536X |
Download Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds Book in PDF, Epub and Kindle
In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 1991 |
Genre | : Differential equations, Partial |
ISBN | : 9780387546773 |
Download Partial Differential Equations Book in PDF, Epub and Kindle
Author | : M.A. Shubin |
Publisher | : Springer Science & Business Media |
Total Pages | : 278 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662067196 |
Download Partial Differential Equations VII Book in PDF, Epub and Kindle
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".
Author | : M.A. Shubin |
Publisher | : Springer |
Total Pages | : 274 |
Release | : 2012-12-22 |
Genre | : Mathematics |
ISBN | : 9783662067208 |
Download Partial Differential Equations VII Book in PDF, Epub and Kindle
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".
Author | : Dmitri Fursaev |
Publisher | : Springer Science & Business Media |
Total Pages | : 294 |
Release | : 2011-06-25 |
Genre | : Science |
ISBN | : 9400702051 |
Download Operators, Geometry and Quanta Book in PDF, Epub and Kindle
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.
Author | : M.A. Shubin |
Publisher | : Springer Science & Business Media |
Total Pages | : 296 |
Release | : 2011-06-28 |
Genre | : Mathematics |
ISBN | : 3642565794 |
Download Pseudodifferential Operators and Spectral Theory Book in PDF, Epub and Kindle
I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.
Author | : Michael Demuth |
Publisher | : Birkhäuser |
Total Pages | : 346 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034882319 |
Download Partial Differential Equations and Spectral Theory Book in PDF, Epub and Kindle
The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.