Non-commutative analysis
The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret'non-commutative analysis'broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C" algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift inva…
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- Full title :Non-commutative analysis / Palle Jorgensen, the University of Iowa, USA ; Feng Tian, Hampton University, USA.
Summary
The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret'non-commutative analysis'broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C" algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
Read More ↓Edition Statements
- Publication Date:©2017
Publication Statements
- Publisher(s):World Scientific Publishing Co Pte Ltd
- Place of Publication:Singapore
- Language:eng
- Publication Date:©2017
The Physical Object
- Description:1 online resource (xxviii, 533 pages)
Edition Identifiers
- ISBN:9789813202139, 9813202130
- oclc:ocn974547145
- LC Classification:QA320
- Dewey Decimal:515/.7
Table of Contents
Subjects and user's guide -- Elementary facts -- Unbounded operators in Hilbert space -- Spectral theory -- GNS and representations -- Completely positive maps -- Brownian motion -- Lie groups, and their unitary representations -- The Kadison-Singer problem -- Selfadjoint extensions -- Unbounded graph-laplacians -- Reproducing kernel Hilbert space.
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