Author : Bin Shao
Publisher :
Page : 210 pages
File Size : 36,35 MB
Release : 1994
Category : Operator equations
ISBN :
Author : Estelle Basor
Publisher : Springer Nature
Page : 606 pages
File Size : 41,63 MB
Release : 2023-01-01
Category : Mathematics
ISBN : 3031138511
This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.
Author : B.-W. Schulze
Publisher : Elsevier
Page : 417 pages
File Size : 16,24 MB
Release : 1991-10-17
Category : Mathematics
ISBN : 0080875459
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics.The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
Author : Aleksandr Vladimirovich Sobolev
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 46,36 MB
Release : 2013-02-26
Category : Mathematics
ISBN : 0821884875
Relying on the known two-term quasiclassical asymptotic formula for the trace of the function $f(A)$ of a Wiener-Hopf type operator $A$ in dimension one, in 1982 H. Widom conjectured a multi-dimensional generalization of that formula for a pseudo-differential operator $A$ with a symbol $a(\mathbf{x}, \boldsymbol{\xi})$ having jump discontinuities in both variables. In 1990 he proved the conjecture for the special case when the jump in any of the two variables occurs on a hyperplane. The present paper provides a proof of Widom's Conjecture under the assumption that the symbol has jumps in both variables on arbitrary smooth bounded surfaces.
Author :
Publisher :
Page : 676 pages
File Size : 13,63 MB
Release : 1989
Category : Operator theory
ISBN :
Author : Stephan Rempel
Publisher :
Page : 426 pages
File Size : 31,17 MB
Release : 1989
Category : Boundary value problems
ISBN :
Author : Günter Lumer
Publisher : De Gruyter Akademie Forschung
Page : 432 pages
File Size : 48,33 MB
Release : 1994
Category : Mathematics
ISBN :
This volume contains the contributions of the conference "Partial Differential Equations" in Han-sur-Lesse, Belgium, December 1993. The originally intended Belgian-French meeting developed into a truely international conference, including specialists from Argentina, Germany, Puerto Rico, Russia, Spain, and the USA. The authors was to discuss a variety of important questions in applied sciences, engineering and mathematical physics which lead to deep structures and new challenges to the analysis of partial differential equations. The articles show the complexity of phenomena for a broader readership in non-linear analysis, free boundary value problems, effects from singularities, asymptotics, and stability of solutions.
Author :
Publisher :
Page : 820 pages
File Size : 21,81 MB
Release : 2003
Category : Mathematics
ISBN :
Author : M.A. Shubin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 24,13 MB
Release : 2011-06-28
Category : Mathematics
ISBN : 3642565794
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 Eugene Taylor
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 23,18 MB
Release : 1984
Category : Differential equations, Hypoelliptic
ISBN : 0821823140
