Analytic functions characterized by their means on an arc

Authors:
Chin Hung Ching and Charles K. Chui

Journal:
Trans. Amer. Math. Soc. **184** (1973), 175-183

MSC:
Primary 30A72

MathSciNet review:
0338375

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Abstract: It is known that a function *f*, holomorphic in the open unit disc *U* with boundary data for some , is uniquely determined by its arithmetic means over equally spaced points on . By using different techniques, we weaken the hypothesis to functions with derivatives, . We also prove that a function is determined by its averages over an arc *K* if *f* is holomorphic in a neighborhood of , and that this result is false for some functions *f* in . On the other hand, we can capture a function from its means and shifted means on *K*.

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DOI:
https://doi.org/10.1090/S0002-9947-1973-0338375-2

Keywords:
Arithmetic means on an arc,
Möbius function,
holomorphic functions,
uniqueness and nonuniqueness,
representation formulas

Article copyright:
© Copyright 1973
American Mathematical Society