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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 401, Pages 103–121 (Mi znsl5229)  
Free multiple interpolation

A. M. Kotochigov

Saint-Petersburg State Electrotechnical University, Saint-Petersburg, Russia
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Abstract: Our aim in this article is to construct a bounded linear operator that solves the problem of multiple interpolation (interpolation with derivatives). It is proved that such an operator exists for nontangential and sparse interpolation sets if we consider interpolation by analytic functions satisfying the following condition: $|f^{(m)}(z_1)-f^{(m)}(z_2)|\leq\omega(|z_1-z_2|)$.
Key words and phrases: analytic function, modulus of continuity, multiple interpolation.
Received: 17.07.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 194, Issue 6, Pages 656–666
DOI: https://doi.org/10.1007/s10958-013-1555-7
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: A. M. Kotochigov, “Free multiple interpolation”, Investigations on linear operators and function theory. Part 40, Zap. Nauchn. Sem. POMI, 401, POMI, St. Petersburg, 2012, 103–121; J. Math. Sci. (N. Y.), 194:6 (2013), 656–666
Citation in format AMSBIB
\Bibitem{Kot12}
\by A.~M.~Kotochigov
\paper Free multiple interpolation
\inbook Investigations on linear operators and function theory. Part~40
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 401
\pages 103--121
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5229}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2981970}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 194
\issue 6
\pages 656--666
\crossref{https://doi.org/10.1007/s10958-013-1555-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899002149}
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