Keywords

l^p-stability, convolution operator, infinite matrices

Abstract

This dissertation originates from a classical result that the lp-stability of the convolution operator associated with a summable sequence are equivalent to each other for different p . This dissertation is motivated by the recent result by C. E. Shin and Q. Sun (Journal ofFunctional Analysis, 256(2009), 2417-2439), where the lp-stability of infinite matrices in the Gohberg-Baskakov-Sjostrand class are proved to be equivalent to each other for different p. In the dissertation, for an infinite matrix having certain off-diagonal decay, its weighted lp-stability for different p are proved to be equivalent to each other and hence a result by Shin and Sun is generalized.

Notes

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Graduation Date

2009

Advisor

Sun, Qiyu

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0002685

URL

http://purl.fcla.edu/fcla/etd/CFE0002685

Language

English

Release Date

September 2009

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

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Included in

Mathematics Commons

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