Recapturing a holomorphic function on an annulus from its mean boundary values

Authors:
Chin Hung Ching and Charles K. Chui

Journal:
Proc. Amer. Math. Soc. **41** (1973), 120-126

MSC:
Primary 30A72

DOI:
https://doi.org/10.1090/S0002-9939-1973-0320326-3

MathSciNet review:
0320326

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Abstract: Let be an annulus in the complex plane with closure and boundary . We prove that a function , holomorphic in with boundary data for some , is uniquely determined by its arithmetic means and over equally spaced points on . We also give an explicit formula for recapturing from its means and . Furthermore, we derive the relations between and which are necessary and sufficient for the analytic continuability of from to the whole disc.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0320326-3

Keywords:
Annulus,
mean boundary values,
Fourier coefficients,
Riemann coefficients,
Riemann series,
Möbius function,
holomorphic function

Article copyright:
© Copyright 1973
American Mathematical Society