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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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History of Functional Analysis, Volume 49 (Hardcover)
Loot Price: R1,348
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History of Functional Analysis, Volume 49 (Hardcover)
Series: North-Holland Mathematics Studies
Expected to ship within 10 - 15 working days
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History of Functional Analysis presents functional analysis as a
rather complex blend of algebra and topology, with its evolution
influenced by the development of these two branches of mathematics.
The book adopts a narrower definition-one that is assumed to
satisfy various algebraic and topological conditions. A moment of
reflections shows that this already covers a large part of modern
analysis, in particular, the theory of partial differential
equations. This volume comprises nine chapters, the first of which
focuses on linear differential equations and the Sturm-Liouville
problem. The succeeding chapters go on to discuss the
""crypto-integral"" equations, including the Dirichlet principle
and the Beer-Neumann method; the equation of vibrating membranes,
including the contributions of Poincare and H.A. Schwarz's 1885
paper; and the idea of infinite dimension. Other chapters cover the
crucial years and the definition of Hilbert space, including
Fredholm's discovery and the contributions of Hilbert; duality and
the definition of normed spaces, including the Hahn-Banach theorem
and the method of the gliding hump and Baire category; spectral
theory after 1900, including the theories and works of F. Riesz,
Hilbert, von Neumann, Weyl, and Carleman; locally convex spaces and
the theory of distributions; and applications of functional
analysis to differential and partial differential equations. This
book will be of interest to practitioners in the fields of
mathematics and statistics.
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