Harmonic analysis : smooth and nonsmooth
 Responsibility
 Palle E.T. Jorgensen.
 Publication
 Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, [2018]
 Physical description
 xi, 266 pages : illustrations ; 26 cm.
 Series
 Regional conference series in mathematics no. 128.
Available online
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA1 .R33 NO.128  Unknown 
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Description
Creators/Contributors
 Author/Creator
 Jørgensen, Palle E. T., 1947 author.
 Contributor
 Conference Board of the Mathematical Sciences.
 National Science Foundation (U.S.)
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 245263) and index.
 Contents

 Introduction. Smooth vs the nonsmooth categories Spectral pair analysis for IFSs Harmonic analyses on fractals, with an emphasis on iterated function systems (IFS) measures Four kinds of harmonic analysis Harmonic analysis via representations of the Cuntz relations $\textit{ Positive definite functions }$ and kernel analysis Representations of $\textit{Lie groups}$. Noncommutative harmonic analysis Bibliography Index.
 (source: Nielsen Book Data)
 Summary

There is a recent and increasing interest in harmonic analysis of nonsmooth geometries. Realworld 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 nonsmooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, $L^2$ spaces derived from appropriate Gaussian processes. The book is based on a series of ten lectures delivered in June 2018 at a CBMS conference held at Iowa State University.
(source: Nielsen Book Data)
Subjects
 Subject
 Harmonic analysis.
 Measure and integration  Classical measure theory  Fractals.
 Quantum theory  General mathematical topics and methods in quantum theory  Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.
 Number theory  Probabilistic theory: distribution modulo $1$; metric theory of algorithms  Harmonic analysis and almost periodicity.
 Probability theory and stochastic processes  Markov processes  Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
 Harmonic analysis on Euclidean spaces  Nontrigonometric harmonic analysis  Wavelets and other special systems.
 Probability theory and stochastic processes  Stochastic processes  Fractional processes, including fractional Brownian motion.
 Dynamical systems and ergodic theory  Ergodic theory  Relations with number theory and harmonic analysis.
 Harmonic analysis on Euclidean spaces  Harmonic analysis in several variables  Harmonic analysis and PDE.
 Harmonic analysis.
 Measure and integration  Classical measure theory  Fractals.
 Quantum theory  General mathematical topics and methods in quantum theory  Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.
 Number theory  Probabilistic theory: distribution modulo $1$; metric theory of algorithms  Harmonic analysis and almost periodicity.
 Probability theory and stochastic processes  Markov processes  Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
 Harmonic analysis on Euclidean spaces  Nontrigonometric harmonic analysis  Wavelets and other special systems.
 Probability theory and stochastic processes  Stochastic processes  Fractional processes, including fractional Brownian motion.
 Dynamical systems and ergodic theory  Ergodic theory  Relations with number theory and harmonic analysis.
 Harmonic analysis on Euclidean spaces  Harmonic analysis in several variables  Harmonic analysis and PDE.
 Harmonic analysis.
Bibliographic information
 Publication date
 2018
 Series
 CBMS regional conference series in mathematics ; number 128
 Note
 "Support from the National Science Foundation."
 "NSFCBMS Regional Conference in the Mathematical Sciences on Harmonic Analysis: Smooth and NonSmooth, held at Iowa State University, June 48, 2018."
 ISBN
 9781470448806 paperback alkaline paper
 1470448807 paperback alkaline paper