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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 5, Pages 1102–1127 (Mi izv2232)  

This article is cited in 14 scientific papers (total in 14 papers)

The multiple interpolation problem in the space of entire functions of given proximate order

A. V. Bratishchev, Yu. F. Korobeinik

Abstract: In this paper criteria are obtained for solvability of the multiple interpolation problem in the class $[\rho(r),\infty)$, where $\rho(r)$ is a proximate order ($\lim_{r\to\infty}\rho(r)=\rho$, $0\leqslant\rho<\infty$) for any sequence from a certain class $\textit Л_{\rho(r)}$ or one of its subclasses. The results are applied to find criteria that the system $ż^{l-1}\exp\lambda_nz$, $l=1,…, p_n\}^\infty_{n=1}$ be a basis in its linear hull.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:5, 1049–1074

Bibliographic databases:

UDC: 517.53
MSC: Primary 30A80, 30A18; Secondary 30A66
Received: 08.10.1975

Citation: A. V. Bratishchev, Yu. F. Korobeinik, “The multiple interpolation problem in the space of entire functions of given proximate order”, Izv. Akad. Nauk SSSR Ser. Mat., 40:5 (1976), 1102–1127; Math. USSR-Izv., 10:5 (1976), 1049–1074

Citation in format AMSBIB
\by A.~V.~Bratishchev, Yu.~F.~Korobeinik
\paper The multiple interpolation problem in the space of entire functions of given proximate order
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 5
\pages 1102--1127
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 5
\pages 1049--1074

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    This publication is cited in the following articles:
    1. A. V. Bratishchev, Yu. F. Korobeinik, “On some characteristics of the growth of subharmonic functions”, Math. USSR-Sb., 34:5 (1978), 603–626  mathnet  crossref  mathscinet  zmath
    2. Yu. F. Korobeinik, “The moment problem, interpolation and basicity”, Math. USSR-Izv., 13:2 (1979), 277–306  mathnet  crossref  mathscinet  zmath  isi
    3. Carlos A. Berenstein, B.A. Taylor, “A new look at interpolation theory for entire functions of one variable”, Advances in Mathematics, 33:2 (1979), 109  crossref
    4. Yu. F. Korobeinik, “Interpolation problems, nontrivial expansions of zero, and representing systems”, Math. USSR-Izv., 17:2 (1981), 299–337  mathnet  crossref  mathscinet  zmath  isi
    5. P. A. Kuchment, “Floquet theory for partial differential equations”, Russian Math. Surveys, 37:4 (1982), 1–60  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. V. Bratishchev, “A type of lower estimate for entire functions of finite order, and some applications”, Math. USSR-Izv., 24:3 (1985), 415–438  mathnet  crossref  mathscinet  zmath
    7. R Sandler, “Convergence of a series of exponentials associated with an entire function”, Journal of Mathematical Analysis and Applications, 117:1 (1986), 220  crossref
    8. N. V. Zabolotskii, M. N. Sheremeta, “On the slow growth of the principal characteristics of entire functions”, Math. Notes, 65:2 (1999), 168–174  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. A. S. Krivosheev, “Interpolation with estimates in $\mathbb C^n$ and its applications”, Sb. Math., 192:9 (2001), 1297–1340  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. A. S. Krivosheev, “A fundamental principle for invariant subspaces in convex domains”, Izv. Math., 68:2 (2004), 291–353  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. O. A. Krivosheeva, A. S. Krivosheev, “Fundamentalnyi printsip dlya invariantnykh podprostranstv”, Ufimsk. matem. zhurn., 2:4 (2010), 58–73  mathnet  zmath  elib
    12. O. A. Krivosheeva, A. S. Krivosheev, “A Criterion for the Fundamental Principle to Hold for Invariant Subspaces on Bounded Convex Domains in the Complex Plane”, Funct. Anal. Appl., 46:4 (2012), 249–261  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. O. A. Bozhenko, K. G. Malyutin, “Problem of multiple interpolation in class of analytical functions of zero order in half-plane”, Ufa Math. J., 6:1 (2014), 18–28  mathnet  crossref  elib
    14. O. A. Bozhenko, A. F. Grishin, K. G. Malyutin, “An interpolation problem in the class of entire functions of zero order”, Izv. Math., 79:2 (2015), 233–256  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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