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On the modulus of boundary values of holomorphic functions

Author: R. Michael Range
Journal: Proc. Amer. Math. Soc. 65 (1977), 282-286
MSC: Primary 32A10
MathSciNet review: 0457758
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Abstract: A differential geometric method is introduced to study the modulus of boundary values of holomorphic functions on smoothly bounded pseudoconvex domains D in $ {{\mathbf{C}}^n},n \geqslant 2$. It is shown that functions in $ A(D)$ are determined up to a constant factor by their modulus on an open subset of the Shilov boundary. For the case of $ {H^\infty }(D)$, it is shown that inner functions which satisfy a certain local condition are constant.

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Keywords: Shilov boundary, pseudoconvex domain, inner function, point of finite type, boundary values of holomorphic functions, CR-manifold, CR-function
Article copyright: © Copyright 1977 American Mathematical Society