Pseudodifferential Operators And Spectral Theory
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Pseudodifferential Operators And Spectral Theory
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Author : M.A. Shubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Pseudodifferential Operators And Spectral Theory written by M.A. Shubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
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.
Pseudodifferential Operators And Spectral Theory
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Author : Mikhail A. Shubin
language : en
Publisher: Springer
Release Date : 1987
Pseudodifferential Operators And Spectral Theory written by Mikhail A. Shubin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
The theory of pseudo differential operators (abbreviated PD~) is compara tively young; in its modern form it was created in the mid-sixties. The progress achieved with its help, however, has been so essential that without PD~ it would indeed be difficult to picture modern analysis and mathematical physics. PD~ are of particular importance in the study of elliptic equations. Even the simplest operations on elliptic operators (e. g. taking the inverse or the square root) lead out of the class of differential operators but will, under reasonable assumptions, preserve the class of PD~. A significant role is played by PD~ in the index theory for elliptic operators, where PD~ are needed to extend the class of possible deformations of an operator. PD~ appear naturally in the reduction to the boundary for any elliptic boundary problem. In this way, PD~ arise not as an end-in-themselves, but as a powerful and natural tool for the study of partial differential operators (first and foremost elliptic and hypo elliptic ones). In many cases, PD~ allow us not only to establish new theorems but also to have a fresh look at old ones and thereby obtain simpler and more transparent formulations of already known facts. This is, for instance, the case in the theory of Sobolev spaces. A natural generalization of PD~ are the Fourier integral operators (abbreviatedFIO), the first version ofwhich was the Maslov canonical operator.
Pseudodifferential Operators And Spectral Theory
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Author : Mikhail Aleksandrovich Shubin
language : en
Publisher: Springer
Release Date : 1987
Pseudodifferential Operators And Spectral Theory written by Mikhail Aleksandrovich Shubin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Pseudodifferential operators categories.
Partial Differential Equations Vii
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Author : M.A. Shubin
language : en
Publisher: Springer
Release Date : 2012-12-22
Partial Differential Equations Vii written by M.A. Shubin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-22 with Mathematics categories.
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".
Partial Differential Equations Vii
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Author : M.A. Shubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Partial Differential Equations Vii written by M.A. Shubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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".
Partial Differential Equations
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Author :
language : en
Publisher:
Release Date : 1991
Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Differential equations, Partial categories.
The Spectral Theory Of Toeplitz Operators
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Author : L. Boutet de Monvel
language : en
Publisher: Princeton University Press
Release Date : 1981-08-21
The Spectral Theory Of Toeplitz Operators written by L. Boutet de Monvel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-08-21 with Mathematics categories.
The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.
Pseudodifferential Operators With Automorphic Symbols
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Author : André Unterberger
language : en
Publisher: Birkhäuser
Release Date : 2015-06-22
Pseudodifferential Operators With Automorphic Symbols written by André Unterberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-22 with Mathematics categories.
The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.
Non Self Adjoint Differential Operators Spectral Asymptotics And Random Perturbations
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Author : Johannes Sjöstrand
language : en
Publisher: Springer
Release Date : 2019-05-17
Non Self Adjoint Differential Operators Spectral Asymptotics And Random Perturbations written by Johannes Sjöstrand and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-17 with Mathematics categories.
The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Spectral Theory Of A Class Of Unitary Pseudodifferential Operators
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Author : Douglas Charles Szajda
language : en
Publisher:
Release Date : 1992
Spectral Theory Of A Class Of Unitary Pseudodifferential Operators written by Douglas Charles Szajda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.