An Introduction to Hilbert Module Approach to Multivariable Operator Theory
by Jaydeb Sarkar
Publisher: arXiv 2013
Number of pages: 52
This article gives an introduction of Hilbert modules over function algebras and surveys some recent developments. Here the theory of Hilbert modules is presented as combination of commutative algebra, complex geometry and the geometry of Hilbert spaces and its applications to the theory of n-tuples of commuting operators.
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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 Alexander C. R. Belton - Lancaster University
These lecture notes are an expanded version of a set written for a course given to final-year undergraduates at the University of Oxford. A thorough understanding of Banach and Hilbert spaces is a prerequisite for this material.
by Ivan F. Wilde - King's College, London
These notes are based on lectures given as part of a 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; etc.
by F.F. Bonsall - Tata Institute Of Fundamental Research
The book is concerned with the application of a variety of methods to both non-linear (fixed point) problems and linear (eigenvalue) problems in infinite dimensional spaces. Author was interested in the construction of eigenvectors and eigenvalues.