Scattering Theory for Orthogonal Wavelets

Palle E.T Jorgensen

doi:10.4324/9781315139548-8

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Book chapter

Scattering Theory for Orthogonal Wavelets

Palle E.T Jorgensen

Clifford Algebras in Analysis and Related Topics, pp.173-198

CRC Press, 1

1999

DOI: 10.4324/9781315139548-8

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Abstract

We apply the Lax-Phillips wave equation scattering theory to multiresolutions associated with wavelets. For wavelet scattering, the translation symmetry, the scaling operator, and the scaling function are identified in the scattering theoretic spectral transform; the scaling function is shown to be analytic; and an analytic spectral function is identified as an invariant for multiresolutions, normalized so that the Haar wavelet corresponds to the constant function. For the study of the functional equation, we introduce almost periodic spaces and establish a general convergence for the infinite product formula with the limit in the L 2-space of the corresponding Bohr group.

Scattering Operator

Orthogonal Wavelet

Scaling Function

Unitary Isomorphism

Haar Wavelet

Outgoing States

Hardy Space

Wave Equation

2π Periodic Function

Haar Measure

Functional Equation

Defect Space

Closed Subspace

Scaling Operator

Translation Group

Integral Translates

Commutation Relation

Proper Inclusion

Clifford Algebras

Dirac Op Erator

Scattering Theory

Spectral Transform

Finite Sum

Paley Wiener Theorem

Hilbert Space

Details

Title: Subtitle: Scattering Theory for Orthogonal Wavelets
Creators: Palle E.T Jorgensen - University of Iowa, Mathematics
Resource Type: Book chapter
Publication Details: Clifford Algebras in Analysis and Related Topics, pp.173-198
Edition: 1
DOI: 10.4324/9781315139548-8
Publisher: CRC Press
Alternative title: Scattering Theory for Orthogonal Wavelets
Language: English
Date published: 1999
Academic Unit: Mathematics
Record Identifier: 9984241158502771

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