Download or read book Second Order Asymptotics for the Discrete Analogue of a Class of Pseudodifferential Operators written by Bin Shao and published by . This book was released on 1994 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Second Order Asymptotics of a Class of Integral Operators with Discontinuous Symbols written by Shuxian Lou and published by . This book was released on 1992 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Toeplitz Operators and Random Matrices written by Estelle Basor and published by Springer Nature. This book was released on 2023-01-01 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain.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.

Download or read book Pseudo Differential Operators Generalized Functions and Asymptotics written by Shahla Molahajloo and published by Springer Science & Business Media. This book was released on 2013-02-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.

Download or read book Pseudodifferential Operators PMS 34 written by Michael Eugene Taylor and published by Princeton University Press. This book was released on 2017-03-14 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here Michael Taylor develops pseudodifferential operators as a tool for treating problems in linear partial differential equations, including existence, uniqueness, and estimates of smoothness, as well as other qualitative properties. Originally published in 1981. 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.

Download or read book Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains written by Harold Widom and published by Springer. This book was released on 2006-11-14 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Pseudo Differential Operators on Manifolds with Singularities written by B.-W. Schulze and published by Elsevier. This book was released on 1991-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Pseudodifferential Operators and Boundary Value Problems for Elliptic Equations and Systems written by George Chkadua and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Pseudo Differential Operators with Discontinuous Symbols Widom s Conjecture written by Aleksandr Vladimirovich Sobolev and published by American Mathematical Soc.. This book was released on 2013-02-26 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Pseudodifferential Operators and Spectral Theory written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Elliptic Operators Topology and Asymptotic Methods written by John Roe and published by Longman Scientific and Technical. This book was released on 1988 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Asymptotics for Elliptic Mixed Boundary Problems written by Stephan Rempel and published by . This book was released on 1989 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reviews in Operator Theory 1980 86 written by and published by . This book was released on 1989 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partial Differential Equations written by Günter Lumer and published by De Gruyter Akademie Forschung. This book was released on 1994 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Noncommutative Microlocal Analysis written by Michael Eugene Taylor and published by American Mathematical Soc.. This book was released on 1984 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Semiclassical Analysis written by Maciej Zworski and published by American Mathematical Soc.. This book was released on 2012 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.