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Müntz-Szasz type approximation and the angular growth of lacunary integral functions


Author: J. M. Anderson
Journal: Trans. Amer. Math. Soc. 169 (1972), 237-248
MSC: Primary 30A82; Secondary 30A64
DOI: https://doi.org/10.1090/S0002-9947-1972-0310259-4
MathSciNet review: 0310259
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Abstract: We consider analogues of the Müntz-Szasz theorem, as in [15] and [4], for functions regular in an angle. This yields necessary and sufficient conditions for the existence of integral functions which are bounded in an angle and have gaps of a very regular nature in their power series expansion. In the case when the gaps are not so regular, similar results hold for formal power series which converge in the angle concerned.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0310259-4
Keywords: Integral functions, linear manifold, complete and incomplete systems of monomials, functions of exponential type
Article copyright: © Copyright 1972 American Mathematical Society

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