Harmonic analysis: smooth and non-smooth

Palle E T Jorgensen

Book

Harmonic analysis: smooth and non-smooth

CBMS regional conference series in mathematics, number 128, Conference Board of the Mathematical Sciences by the American Mathematical Society

2018

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Abstract

There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. Notions of harmonic analysis focus on transforms and expansions and involve dual variables. In this book on smooth and non-smooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis v.

Calculus

Harmonic Analysis

Measure and integration -- Classical measure theory -- Fractals

Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems

Dynamical systems and ergodic theory -- Ergodic theory -- Relations with number theory and harmonic analysis

Probability theory and stochastic processes -- Markov processes -- Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)

Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE

Number theory -- Probabilistic theory: distribution modulo $1$; metric theory of algorithms -- Harmonic analysis and almost periodicity

Quantum theory -- General mathematical topics and methods in quantum theory -- Quantum mechanics on special spaces: manifolds, fractals, graphs, etc

Probability theory and stochastic processes -- Stochastic processes -- Fractional processes, including fractional Brownian motion

Mathematical Analysis

Details

Title: Subtitle: Harmonic analysis: smooth and non-smooth
Creators: Palle E T Jorgensen - University of Iowa, Mathematics
Resource Type: Book
Publisher: Conference Board of the Mathematical Sciences by the American Mathematical Society; Providence, Rhode Island
Series: CBMS regional conference series in mathematics; number 128
ISBN: 9781470448806; 1470448807
Number of pages: xi, 266 pages
Language: English
Date published: 2018
Academic Unit: Mathematics
Record Identifier: 9983995482402771

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