Von Neumann Algebras
by Vaughan F. R. Jones
Publisher: UC Berkeley Mathematics 2010
Number of pages: 159
The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. The philosophy is to lavish attention on a few key results and examples, and we prefer to make simplifying assumptions rather than go for the most general case. Thus we do not hesitate to give several proofs of a single result, or repeat an argument with different hypotheses.
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by Gerald Teschl - University of Vienna
This manuscript provides a brief introduction to nonlinear functional analysis. As an application we consider partial differential equations and prove existence and uniqueness for solutions of the stationary Navier-Stokes equation.
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From the table of contents: Introduction; The spaces S and S'; The spaces D and D'; The Fourier transform; Convolution; Fourier-Laplace Transform; Structure Theorem for Distributions; Partial Differential Equations; and more.
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This book at the beginning graduate level will help students with primary interests elsewhere to acquire a facility with tools of a functional analytic flavor, say in harmonic analysis, numerical analysis, stochastic processes, or in physics.
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