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Field name	Details
Dewey Class	515.782
Title	Distributions and Operators ([EBook]) / by Gerd Grubb.
Author	Grubb, Gerd
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 2009.
Physical Details	XII, 464 pages : online resource.
Series	Graduate texts in mathematics 0072-5285 ; ; 252
ISBN	9780387848952
Summary Note	This book gives an introduction to distribution theory, in the spirit of Laurent Schwartz. Additionally, the aim is to show how the theory is combined with the study of operators in Hilbert space by methods of functional analysis, with applications to partial and ordinary differential equations. Here, the author provides an introduction to unbounded operators in Hilbert space, including a complete theory of extensions of operators, and applications using contraction semigroups. In more advanced parts of the book, the author shows how distribution theory is used to define pseudodifferential operators on manifolds, and gives a detailed introduction to the pseudodifferential boundary operator calculus initiated by Boutet de Monvel, which allows a modern treatment of elliptic boundary value problems. This book is aimed at graduate students, as well as researchers interested in its special topics, and as such, the author provides careful explanations along with complete proofs, and a bibliography of relevant books and papers. Each chapter has been enhanced with many exercises and examples. Unique topics include: * the interplay between distribution theory and concrete operators; * families of extensions of nonselfadjoint operators; * an illustration of the solution maps between distribution spaces by a fully worked out constant-coefficient case; * the pseudodifferential boundary operator calculus; * the CalderÃ³n projector and its applications. Gerd Grubb is Professor of Mathematics at University of Copenhagen.:
Contents note	Preface -- Motivation and overview -- Function spaces and approximation -- Distributions: Examples and rules of calculus -- Realizations and Sobolev spaces -- Fourier transformation of distributions -- Applications to differential operators: The Sobolev theorem -- Pseudodifferential operators on open sets -- Pseudodifferential operators on manifolds, index of elliptic operators -- Boundary value problems in a constant-coefficient case -- Pseudodifferential boundary operators -- Pseudodifferential methods for boundary value problems -- Unbounded linear operators -- Families of extensions -- Semigroups of operators -- Some notation and prerequisites -- Topological vector spaces -- Function spaces on sets with smooth boundary -- Bibliography -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-387-84895-2
Links to Related Works	Subject References: Differential equations, Partial . Functional Analysis . Mathematics . Operator Theory . Partial differential equations . Authors: Grubb, Gerd . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 515.782 .

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Distributions and Operators

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