Journal ArticleDOI
The multiple interpolation problem in the space of entire functions of given proximate order
A V Bratiščev,Ju F Korobeĭnik +1 more
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In this paper, criteria are obtained for solvability of the multiple interpolation problem in the class, where is a proximate order (, ) for any sequence from a certain class or one of its subclasses.Abstract:
In this paper criteria are obtained for solvability of the multiple interpolation problem in the class , where is a proximate order (, ) for any sequence from a certain class or one of its subclasses. The results are applied to find criteria that the system , be a basis in its linear hull.Bibliography: 14 titles.read more
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Book
Floquet Theory for Partial Differential Equations
TL;DR: In this article, the authors introduce the concept of Holomorphic Fredholm operator functions, which are operators that depend holomorphically on a parameter and have been shown to be able to handle infinite-dimensional complex analysis problems.
Journal ArticleDOI
A new look at interpolation theory for entire functions of one variable
TL;DR: The existence of solutions of the inhomogeneous Cauchy-Riemann equations as a powerful tool in the study of analytic functions of several complex variables is well demonstrated in this article.
Journal ArticleDOI
Interpolation problems, nontrivial expansions of zero, and representing systems
TL;DR: In this article, it was shown that for a convex domain with support function and distinct complex numbers to be absolutely representing in the space of functions analytic in, with the topology of uniform convergence on compact sets, it is necessary and sufficient that either of the following two conditions hold: 1) the system has a nontrivial expansion of zero in, i.e.
Journal ArticleDOI
The moment problem, interpolation and basicity
TL;DR: In this paper, the authors present criteria for the solvability of the general moment problem in countably Hilbert spaces and the relationship between the general interpolation problem in reflexive spaces and corresponding moment problem is also established.
Journal ArticleDOI
Problem of multiple interpolation in class of analytical functions of zero order in half-plane
TL;DR: In this article, the authors considered the problem of multiple interpolation in a class of functions of a zero order and type not exceeding normal in the upper half-plane of the complex variable.
References
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Book ChapterDOI
Topologische lineare Räume
TL;DR: In this article, the elementare Theorie der normierten Raume and der Banachraume is discussed, in which anzahl klassischer Beispiele wird diskutiert, die in den spateren Teilen des Buches immer wieder herangezogen werden.
Journal ArticleDOI
A Fourier series method for meromorphic and entire functions
Lee A. Rubel,B. A. Taylor +1 more
TL;DR: In this article, it was shown that a growth function X(r) is a function defined for 0, r < <*> that is positive, nondecreasing, and continuous.
Journal ArticleDOI
Representation of Functions by Generalized Dirichlet Series
TL;DR: In this article, it was shown that a function whose coefficients in the series are all zero must itself be zero, and conditions under which the series, or a subsequence of its partial sums, converges to the corresponding function.