Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains PDF Download

Author: Harold Widom
Publisher: Springer
ISBN: 3540396411
Category : Mathematics
Languages : en
Pages : 155

View

Book Description

Author: Man Wah Wong
Publisher: World Scientific
ISBN: 9789810238131
Category : Mathematics
Languages : en
Pages : 156

View

Book Description
In this new edition of An Introduction to Pseudo-Differential Operators, the style & scope of the original book are retained. A chapter on the interchange of order of differentiation & integration is added at the beginning to make the book more self-contained, & a chapter on weak solutions of pseudo-differential equations is added at the end to enhance the value of the book as a work on partial differential equations. Several chapters are provided with additional exercises. The bibliography is slightly expanded & an index is added. Contents: Differentiation of Integrals Depending on Parameters; The Convolution; The Fourier Transform; Tempered Distributions; Symbols, Pseudo-Differential Operators & Asymptotic Expansions; A Partition of Unity & Taylor's Formula; The Product of Two Pseudo-Differential Operators; The Formal Adjoint of a Pseudo-Differential Operator; The Parametrix of an Elliptic Pseudo-Differential Operator; Lp-Boundedness of Pseudo-Differential Operators, 1

Author: M.A. Shubin
Publisher: Springer Science & Business Media
ISBN: 3642565794
Category : Mathematics
Languages : en
Pages : 296

View

Book Description
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: George Chkadua
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

View

Book Description
We investigate asymptotics of fundamental solutions of the hypoelliptic differential equation where the corresponding characteristic polynomial has real multiple zeros. Based on the asymptotic expansion of a fundamental solution we introduce asymptotic classes of distributions and prove existence and uniqueness of solutions in those classes. Our results imply in particular, a new uniqueness theorem for the classical Helmhotz equation. We study a model of fluid-solid acoustic interaction when a piezo-ceramic elastic body ( n+) is embedded in an unbounded fluid domain ( n-). In the bounded domain n+, we have 4 x 4 dimensional matrix strongly elliptic second order partial differential equation, while in the unbounded complement domain n- we have a scalar Helmholtz equation describing acoustic wave propagation. We consider the Dirichlet (Dw), Neumann (Nw) and mixed type (Mw) interaction problems. The physical kinematic and dynamic relations are described mathematically by appropriate boundary and transmission conditions. With the help of the boundary integral equations method and theory of pseudodifferential equations based on the Wiener-Hopf factorization method, we prove uniqueness and existence theorems in Sobolev-Slobodetskii spaces. We derive asymptotic expansions of solutions of the mixed type interaction problem near the line where different boundary conditions meet, and on the basis of our asymptotic analysis, we establish optimal Holder smoothness results for solutions. We also consider three-dimensional Riquier-type and classical mixed boundary value problems for the polymetaharmonic equation We prove existence and uniqueness theorems in Sobolev-Slobodetskii spaces, analyse asymptotic properties of solutions and establish optimal H6lder smoothness results for solutions.

Author: IUrii Vladimirovich Egorov
Publisher: Birkhauser
ISBN: 9783764354848
Category : Mathematics
Languages : en
Pages : 349

View

Book Description
This book grew out of lecture notes based on the DMV seminar "Pseudo- Differential Operators, Singularities, Applications" held by the authors in Reisenburg-GA1/4nzburg, 12a "19 July 1992. The modern theory of elliptic boundary value problems in domains having conical or edge singularities on the boundary as well as the classical theory of elliptic boundary value problems and the original Kondratiev theory are presented. This material forms the foundation for the second part of the book which contains a new construction of pseudo-differential operators with symbols corresponding to the singularities of the boundary of different dimensions. This allows in particular to obtain complete asymptotic expansions of solutions near these singularities.

Author: Heinz O. Cordes
Publisher: Springer
ISBN: 3540478868
Category : Mathematics
Languages : en
Pages : 495

View

Book Description

Author: S D Zaidman
Publisher: CRC Press
ISBN: 9780582277823
Category : Mathematics
Languages : en
Pages : 132

View

Book Description
This Research Note presents in a clear and detailed manner a certain group of results pertaining to some variants, extensions and generalizations on the theory of pseudo-differential operators as introduced in the pioneering work of Kohn-Nirenberg. The author presents a discussion of concepts of order, true order and asymptotic expansions for general linear operators in some vector spaces, following a pattern appearing in pseudo-differential operator theory. The book is intended mainly for an audience of operator theorists, at a fairly elementary level; its main objective a unitary presentation of articles written by the author over a number of years.

Author: Johannes Sjöstrand
Publisher: Springer
ISBN: 3030108198
Category : Mathematics
Languages : en
Pages : 496

View

Book Description
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.

Author: Alexander Nagel
Publisher: Princeton University Press
ISBN: 1400870488
Category : Mathematics
Languages : en
Pages : 167

View

Book Description
The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author: Nguyen Minh Chuong
Publisher: Springer
ISBN: 3319774735
Category : Mathematics
Languages : en
Pages : 368

View

Book Description
This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields. Aimed at graduate students and researchers interested in harmonic analysis over local fields, the topics covered in this book include pseudodifferential operators of principal type and of variable order, semilinear degenerate pseudodifferential boundary value problems (BVPs), non-classical pseudodifferential BVPs, wavelets and Hardy spaces, wavelet integral operators, and wavelet solutions to Cauchy problems over the real field and the p-adic field.