Weighted Lp-stability For Localized Infinite Matrices
نویسندگان
چکیده
This dissertation originates from a classical result that the `-stability of the convolution operator associated with a summable sequence are equivalent to each other for 1 ≤ p ≤ ∞. This dissertation is motivated by the recent result by C. E. Shin and Q. Sun (Journal of Functional Analysis, 256(2009), 2417–2439), where the `-stability of infinite matrices in the Gohberg-Baskakov-Sjöstrand class are proved to be equivalent to each other for different 1 ≤ p ≤ ∞. In the dissertation, for an infinite matrix having certain off-diagonal decay, its weighted `-stability for different 1 ≤ p ≤ ∞ are proved to be equivalent to each other and hence a result by Shin and Sun is generalized.
منابع مشابه
Stability of Localized Operators
Let `p, 1 ≤ p ≤ ∞, be the space of all p-summable sequences and Ca be the convolution operator associated with a summable sequence a. It is known that the `pstability of the convolution operator Ca for different 1 ≤ p ≤ ∞ are equivalent to each other, i.e., if Ca has `p-stability for some 1 ≤ p ≤ ∞ then Ca has `q-stability for all 1 ≤ q ≤ ∞. In the study of spline approximation, wavelet analysi...
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