Some preliminary results about entire functions and distributions are presented. Topics include: entire functions with growth restrictions, a biorthogonality property for entire functions, Cauchy-type estimates of holomorphic functions, the Titchmarsh theorem on supports of convolutions, the Paley–Wiener–Schwartz theorem, and the Ehrenpreis–Hörmander characterization of invertible distributions. These results will be used many times in the later chapters.


Holomorphic Function Entire Function Convolution Equation Nonempty Open Subset Nonempty Compact Subset 
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Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.Mathematical DepartmentDonetsk National UniversityDonetskUkraine

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