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Uniqueness sets for complete orthonormal systems

✍ Scribed by G. G. Gevorkyan

Publisher
SP MAIK Nauka/Interperiodica
Year
1982
Tongue
English
Weight
195 KB
Volume
32
Category
Article
ISSN
0001-4346

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## Abstract Given an orthonormal system __B__ in some __L__^2^(__u__) we consider the operator ideals II~B~ and __T__~B~ of __B__‐summing and __B__‐type operators and some related ideals. We characterize by certain weak compactness properties when II~B~ is equal to the operator ideal II~2~ of 2‐sum

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It is shown that the discrete Calderón condition characterizes completeness of orthonormal wavelet systems, for arbitrary real dilations. That is, if a > 1, b > 0, and the system = {a j/2 ψ(a j xbk) A new proof of the Second Oversampling Theorem is found, by similar methods.