An Analogue of Smirnov's Theorem in Spaces of the Functions which are Inductive Limits of some Hölder Spaces

Abstract:

Both the theory of functions of a complex variable, and the approximation theory, are finding more and more applications in modern engineering sciences. In the present report we consider the spaces of analytic functions inside the unit circle satisfying on the boundary a strong Hölder condition for a rather wide class of the modulus of continuity. An analog of Smirnov's classical theorem relating to Hardy spaces has been obtained. The result is generalized to spaces of functions that are inductive limits of the spaces stated above.

• Periodical: Materials Science Forum (Volume 931)
• Pages: 184-187
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.931.184
• Online since: September 2018
• Authors: Oleg V. Grober, Tatyana A. Grober, Andrey B. Bychkov*
• Keywords: Banach Space, Hölder Functions, Inductive Limit, Locally Convex Space, Modulus of Continuity, Strong Hӧlder Conditions, Zigmund-Bari-Stechkin Conditions

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DOI: 10.1007/bf02675370

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