Orthonormal Sequences in L(r) and Time Frequency Localization
نویسنده
چکیده
We prove that there does not exist an orthonormal basis {bn} for L(R) such that the sequences {μ(bn)}, {μ(c bn)}, and {∆(bn)∆( bn)} are bounded. A higher dimensional version of this result that involves generalized dispersions is also obtained. The main tool is a time-frequency localization inequality for orthonormal sequences in L(R). On the other hand, for d > 1 we construct a basis {bn} for L(R) such that the sequences {μ(bn)}, {μ(c bn)}, and {∆(bn)∆(c bn)} are bounded.
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