Abstract
We investigate symmetric bases of exponential functions in the closure of their linear span in the spaces Lp(μβ) and ℓp(πβ) where αμβ=tβαt, t<0, and νβ({K})=(K+1)β, K∈{0,1,2,...}. We also consider the dual problem of free interpolation in the corresponding Banach Lp-spaces of analytic functions. In many cases one gives the complete description of bases of exponential functions (in the closure of its linear span) in the above-indicated spaces and the solution of the corresponding problems of free interpolation by analytic functions.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN.SSSR, Vol. 65, pp. 17–68, 1976.
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Vinogradov, S.A. Exponential bases and free interpolation in banach spaces with the Lp-norm. J Math Sci 16, 1060–1095 (1981). https://doi.org/10.1007/BF02427717
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DOI: https://doi.org/10.1007/BF02427717