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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Distributions and Operators (Hardcover, 2009 ed.)
Loot Price: R2,580
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Distributions and Operators (Hardcover, 2009 ed.)
Series: Graduate Texts in Mathematics, 252
Expected to ship within 9 - 17 working days
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This textbook gives an introduction to distribution theory with
emphasis on applications using functional analysis. In more
advanced parts of the book, pseudodi?erential methods are
introduced. Distributiontheoryhasbeen
developedprimarilytodealwithpartial(and ordinary) di?erential
equations in general situations. Functional analysis in, say,
Hilbert spaces has powerful tools to establish operators with good
m- ping properties and invertibility properties. A combination of
the two allows showing solvability of suitable concrete partial
di?erential equations (PDE). When partial di?erential operators are
realized as operators in L (?) for 2 n anopensubset?ofR,
theycomeoutasunboundedoperators.Basiccourses
infunctionalanalysisareoftenlimitedtothestudyofboundedoperators,
but we here meet the necessityof treating suitable types
ofunbounded operators; primarily those that are densely de?ned and
closed. Moreover, the emphasis in functional analysis is often
placed on selfadjoint or normal operators, for which beautiful
results can be obtained by means of spectral theory, but the cases
of interest in PDE include many nonselfadjoint operators, where
diagonalizationbyspectraltheoryisnotveryuseful.Weincludeinthisbooka
chapter on unbounded operatorsin Hilbert space (Chapter 12), where
classes of convenient operators are set up, in particular the
variational operators, including selfadjoint semibounded cases
(e.g., the Friedrichs extension of a symmetric operator), but with
a much wider scope. Whereas the functional analysis de?nition of
the operators is relatively clean and simple, the interpretation to
PDE is more messy and complicate
General
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