Description
Book SynopsisThis book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.
Trade ReviewFrom the reviews:
"The book is directed at graduate students and ‘researchers interested in its special topics’ … . Distribution and Operators is split into five parts … . Well-written and scholarly, and equipped with many exercises of considerable pedagogical importance … Grubb’s book is a fine contribution to the literature and should soon occupy a solid place among graduate texts for aspiring hard analysts specializing, e.g., in PDE." (Michael Berg, MAA Online, December, 2008)
“This textbook gives a very clear introduction to distribution theory with emphasis on applications using functional analysis. In more advanced parts of the book, pseudodifferential methods are introduced, specially tailored for the study of boundary value problems. … The whole book is carefully and nicely written and each chapter ends with a number of exercises … . perfect for a Ph.D. course … . most of the material has been used frequently at the University of Copenhagen for several graduate courses.” (Fabio Nicola, Mathematical Reviews, Issue 2010 b)
“The book under review is a complete self-contained introduction to classical distribution theory with applications to the study of linear partial differential operators and, in particular, of (elliptic) boundary value problems, an area where the author has much experience … . very clear and precise. Almost all the results given in the book are proved, and the proofs give plenty of details and are easy to follow. There are a lot of examples and exercises … .” (David Jornet, Zentralblatt MATH, Vol. 1171, 2009)
Table of ContentsDistributions and derivatives.- Motivation and overview.- Function spaces and approximation.- Distributions. Examples and rules of calculus.- Extensions and applications.- Realizations and Sobolev spaces.- Fourier transformation of distributions.- Applications to differential operators. The Sobolev theorem.- Pseudodifferential operators.- Pseudodifferential operators on open sets.- Pseudodifferential operators on manifolds, index of elliptic operators.- Boundary value problems.- Boundary value problems in a constant-coefficient case.- Pseudodifferential boundary operators.- Pseudodifferential methods for boundary value problems.- Topics on Hilbert space operators.- Unbounded linear operators.- Families of extensions.- Semigroups of operators.
