l^p-stability, convolution operator, infinite matrices
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.
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Doctor of Philosophy (Ph.D.)
College of Sciences
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Shi, Qiling, "Weighted Lp-stability For Localized Infinite Matrices" (2009). Electronic Theses and Dissertations, 2004-2019. 3924.