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Complex Analysis, Operators, and Related Topics pp 179–194Cite as

Birkhäuser

Interpolation Sets for the Hölder Spaces of Functions Analytic in a Strip

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 113))

Abstract

A full description of the free interpolation sets is obtained for the analytic Hölder classes in a strip in the complex plane; by a free interpolation set we mean a set such that any Hölder function on this set is the trace of some function belonging to the analytic Hölder class in the strip. A set is an interpolation set if and only if its inner part is sparse and in every boundary interval (of length less then 1) there is a “big” subinterval free from the points of the interpolation set.

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References

  1. Dyn’kin E. M., Sets of free interpolation for Hölder classes, Mat. Sb. 109 (1979), 107–128.

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Author information

Authors and Affiliations

  1. Department of Mathematics, SPb Electrotechnical University, Prof. Popova str. 5, Saint-Petersburg, 197376, Russia

    A. M. Kotochigov

Authors
  1. A. M. Kotochigov
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Editor information

Editors and Affiliations

  1. Department of Mathematics, St. Petersburg University, Bibliotechnaia pl. 2, 198904, Stary Peterhof, St. Petersburg, Russia

    Victor P. Havin

  2. Laboratoire de Mathématiques Pures, UFR de Mathématiques et Informatique Université de Bordeaux I, 351, cours de la Libération, 33405, Talence Cedex, France

    Nikolai K. Nikolski

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© 2000 Springer Basel AG

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Kotochigov, A.M. (2000). Interpolation Sets for the Hölder Spaces of Functions Analytic in a Strip. In: Havin, V.P., Nikolski, N.K. (eds) Complex Analysis, Operators, and Related Topics. Operator Theory: Advances and Applications, vol 113. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8378-8_15

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  • DOI: https://doi.org/10.1007/978-3-0348-8378-8_15

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9541-5

  • Online ISBN: 978-3-0348-8378-8

  • eBook Packages: Springer Book Archive

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