Theory and Applications of the Phi Transform Wavelets.

Abstract

A fundamental idea in Fourier analysis is that the Fourier Transform gives a simultaneous diagonalization of a small but very important class of operators including differentiation and integration. On the other hand, the Fourier Transform is not well suited for studying Multiplication operators. The wavelet transform (and related transforms give excellent simultaneous almost diagonalization of a very large class of operators which includes differentiation, integration, and multiplication: in fact, more-generally singular integral operators and pseudo-differential operators. Professor Rochberg's recent work has been to use this fact to study such operators. Some work has been in the real variable tradition, other parts have involved operators on spaces of analytic functions.

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Document Details

Document Type
Technical Report
Publication Date
Dec 31, 1993
Accession Number
ADA279943

Entities

People

  • Guido Weiss

Organizations

  • Washington University in St. Louis

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Analytic Functions
  • Complex Variables
  • Computational Science
  • Decomposition
  • Differential Equations
  • Digital Signal Processing
  • Equations
  • Fluid Dynamics
  • Fourier Analysis
  • Integral Equations
  • Integrals
  • Mathematics
  • Real Variables
  • Signal Processing
  • Theorems
  • Wavelet Transforms

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis

Technology Areas

  • Space