This article is cited in 4 scientific papers (total in 4 papers)
Extension of entire functions of completely regular growth and right inverse to the operator of representation of analytic functions by quasipolynomial series
Abstract:
Let LL be an entire function of one complex variable that has exponential type, completely regular growth, and whose conjugate diagram is equal to the sum of the closure of a bounded convex domain GG and a convex compact subset KK of C. Criteria ensuring that the operator R of the representation of analytic functions in G by quasipolynomial series with zeros of the function L as exponents has a continuous linear right inverse are established. These criteria are stated in terms of conformal maps of the unit disc onto the domain G and of the exterior of the closed unit disc onto the exterior of K, and of extensions of the original function L to an entire function Q of two complex variables whose absolute value satisfies certain (upper) estimates. An analogue of the Leont'ev interpolation function defined by this extension Q is used to obtain formulae for the continuous linear right inverse to the representation operator R.
Citation:
S. N. Melikhov, “Extension of entire functions of completely regular growth and right inverse to the operator of representation of analytic functions by quasipolynomial series”, Sb. Math., 191:7 (2000), 1049–1073
\Bibitem{Mel00}
\by S.~N.~Melikhov
\paper Extension of entire functions of completely regular growth and right inverse to the~operator of representation of analytic functions by quasipolynomial series
\jour Sb. Math.
\yr 2000
\vol 191
\issue 7
\pages 1049--1073
\mathnet{http://mi.mathnet.ru/eng/sm494}
\crossref{https://doi.org/10.1070/sm2000v191n07ABEH000494}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1809931}
\zmath{https://zbmath.org/?q=an:0995.30019}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000165473200006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034341535}
Linking options:
https://www.mathnet.ru/eng/sm494
https://doi.org/10.1070/sm2000v191n07ABEH000494
https://www.mathnet.ru/eng/sm/v191/i7/p105
This publication is cited in the following 4 articles:
S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, J. Math. Sci. (N. Y.), 257:2 (2021), 206–245
O. A. Ivanova, S. N. Melikhov, “On A. F. Leont'ev's interpolating function”, Ufa Math. J., 6:3 (2014), 17–27
S. N. Melikhov, S. Momm, “On the expansions of analytic functions on convex locally closed sets in exponential series”, Vladikavk. matem. zhurn., 13:1 (2011), 44–58
V. A. Varziev, S. N. Melikhov, “O koeffitsientakh ryadov eksponent dlya analiticheskikh funktsii polinomialnogo rosta”, Vladikavk. matem. zhurn., 13:4 (2011), 18–27