Approximation by polynomials in and another function

Author:
Kenneth John Preskenis

Journal:
Proc. Amer. Math. Soc. **68** (1978), 69-74

MSC:
Primary 30A82

DOI:
https://doi.org/10.1090/S0002-9939-1978-0457740-6

MathSciNet review:
0457740

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Abstract: We present some progress in the understanding of when and why polynomials in *z* and a given continuous function *f* are uniformly dense in all continuous complex valued functions on the closed unit disk. The first theorem requires that *f* be an -function in a neighborhood of the disk which satisfies almost everywhere and is countable for each *a*. The second theorem requires that *f* have a special form and satisfy everywhere except at the origin. The form is that where is a complex valued function of a real variable satisfying is continuous in [0, 1], exists in (0, 1) and where *k* is a positive integer.

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0457740-6

Article copyright:
© Copyright 1978
American Mathematical Society