The analysis of linear partial differential operators. II: Differential operators with constant coefficients
type: Item
instance of: scholarly article
title: The analysis of linear partial differential operators. II: Differential operators with constant coefficients
zbMATH Open document ID: 1062.35004
author: Lars Hörmander
published in: Classics in Mathematics
publication date: 2004-12-22T00:00:00Z
review text: This is a paperback edition of the 1990 edition of the second Volume of the author's treatise on ``The analysis of linear partial differential operators'' (1990; Zbl 0687.35002). In the revised 1990 printing of Volume II, a number of minor flaws were corrected and the bibliography was updated and slightly enlarged. The paperback edition makes this volume more accessible. Volume II is mainly devoted to partial differential operators with constant coefficients and convolution operators, with the exception of Chapter XIII which treats differential operators with constant strength. One of the main tools is Fourier Laplace transform We refer the reader to the excellent, detailed review [Grundlehren der Mathematischen Wissenschaften, 257. (Berlin Heidelberg-New York-Tokyo: Springer-Verlag) (1983; Zbl 0521.35002)]. The chapters in this volume, as the entire treatise, are excellently written, and make a rich, interesting and profitable reading. Since their publication these volumes have been a main reference for anyone working in the theory of linear partial different operators. Among many other authors, recent contributions on the theory of linear partial differential operators with constant coefficients and convolution operators on spaces of (ultra)distributions or spaces of real analytic functions have been obtained by C. Berenstein, R. Braun, P. Domanski, T. Gramchev, H. Komatsu, M. Langenbruch, R. Meise, A. Meril, N. Ortner, V. Palamodov, S. Pilipović, L. Rodino, D. C. Struppa, B. A. Taylor, D. Vogt and P. Wagner. See the joint ``Looking back''-review by Niels Jacob in Zbl 0712.35001.
reviewed by: José Bonet
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35Exx
Mathematics Subject Classification ID: 42A38
zbMATH DE Number: 2123716
zbMATH Keywords: convolution operators
zbMATH Keywords: hypoelliptic operators
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Fourier Laplace transform
zbMATH Keywords: fundamental solutions
zbMATH Keywords: existence and approximation of solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2123716