Basic Analysis Gently Done: Topological Vector Spaces
by Ivan F. Wilde
Publisher: King's College, London 2010
Number of pages: 129
These notes are based on lectures given at King's College London (as part of the Mathematics MSc program). The approach here is to discuss topological vector spaces - with normed spaces considered as special cases. Contents: Topological Spaces; Nets; Product Spaces; Separation; Vector Spaces; Topological Vector Spaces; Locally Convex Topological Vector Spaces; Banach Spaces; The Dual Space of a Normed Space; Frechet Spaces.
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by John Erdos - King's College London
These are notes for a King's College course to fourth year undergraduates and MSc students. They cover the theoretical development of operators on Hilbert space up to the spectral theorem for bounded selfadjoint operators.
by Ivan F Wilde
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.
by Leif Mejlbro - BookBoon
Examples of Hilbert-Smith operators and other types of integral operators, Hilbert Schmidt norm, Volterra integral operator, Cauchy-Schwarz inequality, Hoelder inequality, iterated kernels, Hermitian kernel, and much more.
by Vladimir V. Kisil - University of Leeds
Contents: Fourier Series; Basics of Linear Spaces; Orthogonality; Fourier Analysis; Duality of Linear Spaces; Operators; Spectral Theory; Compactness; The spectral theorem for compact normal operators; Applications to integral equations; etc.