On exponential bases for the Sobolev spaces over an interval |
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Authors: | David L Russell |
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Institution: | Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 U.S.A. |
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Abstract: | We suppose that K is a countable index set and that is a sequence of distinct complex numbers such that forms a Riesz (strong) basis for L2a, b], a < b. Let Σ = {σ1, σ2,…, σm} consist of m complex numbers not in Λ. Then, with p(λ) = Πk = 1m (λ ? σk), forms a Riesz (strong) bas Sobolev space Hma, b]. If we take σ1, σ2,…, σm to be complex numbers already in Λ, then, defining p(λ) as before, forms a Riesz (strong) basis for the space H?ma, b]. We also discuss the extension of these results to “generalized exponentials” tneλkt. |
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