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Integral representation of functions of class K a

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Topics in Interpolation Theory

Part of the book series: Operator Theory Advances and Applications ((OT,volume 95))

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Abstract

An extension problem of M.G. Krein, in which a continuous positive definite kernel of a certain form is specified on a square, is analyzed by a general method which V.P. Potapov developed for solving interpolation problems. The key step is to identify all solutions of the original extension problem with the solutions of an associated Fundamental Matrix Inequality. [Abstract added by editors.]

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References

  1. Krein M.G., About one general method of decompositions of the positive-definite kernels on elementary products, Dokl. Akad. Nauk SSSR 53 (1950) 1125–1128.

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  2. Kovalishina I.V., Analytic theory of a class of interpolation problems, Izv. Akad. Nauk SSSR, 47 (1983) 455–497.

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  3. Kovalishina I.V. and Potapov V.P., Integral representation of Hermitian positive functions, deposited in VINITI.-1981.-1–120.

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  4. Katsnelson V.E., Continual analogues of the Hamburger-Nevanlinna theorem and fundamental matrix inequalities for the classical problems 1., Theor. Func. Anal. Pril. 36 (1981) 31–48.

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  5. Akhiezer N.I., The Classical Problem of Moments and Some Related Topics in Analysis, Fizmatgiz, Moskow, 1961. ( Translation: Hafner, New York, 1965 ).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Kharkov State Academy of Railway Transport, Feuerbach Square 7, Kharkov, 310050, Ukraine

    I. V. Kovalishina

Authors
  1. I. V. Kovalishina
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Editor information

Editors and Affiliations

  1. Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    H. Dym  & V. Katsnelson  & 

  2. Mathematisches Institut, Universität Leipzig, 04109, Leipzig, Germany

    B. Fritzsche  & B. Kirstein  & 

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© 1997 Springer Basel AG

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Kovalishina, I.V. (1997). Integral representation of functions of class K a . In: Dym, H., Katsnelson, V., Fritzsche, B., Kirstein, B. (eds) Topics in Interpolation Theory. Operator Theory Advances and Applications, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8944-5_15

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  • DOI: https://doi.org/10.1007/978-3-0348-8944-5_15

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9838-6

  • Online ISBN: 978-3-0348-8944-5

  • eBook Packages: Springer Book Archive

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