Book: Functional Calculus of Pseudo-Differential Boundary Problems (Progress in Mathematics)
Author: G. Grubb
Pages: 511
Format: DjVu
Language: English
ISBN10: 0817633499
Pseudo differential methods are central to the study of partial differential equations, because they permit an 'algebraization', a replacement of compositions of operators in n-space by simpler product rules for their symbols. The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary value problems via a resolvent construction. A secondary purpose is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by Boutet de Monvel and in a global version, as well as in versions containing a parameter running in an unbounded set. And finally, the book presents some applications to evolution problems, fractional powers, index theory, spectral theory and singular perturbation theory.
In this second edition, the author has extended the theory - with or without a parameter - to operators and symbols with global estimates in the space variables, thus allowing treatment of operators on suitable noncompact manifolds. Thus the book continues to be of interest to research mathematicians and to graduate students studying partial differential equations and pseudodifferential operators. --This text refers to an alternate Hardcover edition.
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