Accession Number:

ADA279943

Title:

Theory and Applications of the Phi Transform Wavelets.

Descriptive Note:

Final rept. 1 Jul 90-31 Dec 93,

Corporate Author:

WASHINGTON UNIV ST LOUIS MO

Personal Author(s):

• Weiss, Guido

Report Date:

1993-12-31

Pagination or Media Count:

11.0

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 Rochbergs 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.

Descriptors:

• *OPERATORS(MATHEMATICS)
• *FOURIER ANALYSIS
• FOURIER TRANSFORMATION
• MATRICES(MATHEMATICS)
• INTEGRALS
• ANALYTIC FUNCTIONS
• REAL VARIABLES
• COMPLEX VARIABLES
• MULTIPLICATION
• SCHRODINGER EQUATION
• KERNEL FUNCTIONS
• INTEGRATION

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE