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A. M. Kotochigov 《Journal of Mathematical Sciences》1978,9(2):274-276
In this paper one considers the following classes of functions, analytic in the circle of the complex plane: , . One establishes that the well-known Carleson condition is necessary and sufficient for the solvability of the interpolation problems, intrinsic for the given class, on sets lying along a ray. In this connection, the class of sequences to be interpolated is described in terms of divided differences of order S. See also author's paper, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,30, 167–169 (1972). 相似文献
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G. Ya. Bomash 《Journal of Mathematical Sciences》1987,36(3):301-314
One considers the following problem. Let X be the space of smooth functions on the circumference and let Y be the space of functions analytic in the disk and smooth up to the boundary. One has to find necessary and sufficient conditions on the closed subset E of the circumference that ensure the inclusionX¦Ey¦E. The problem is solved in the case when the space X is a Carleman class and Y is either an analytic Carleman class having weaker smoothness properties than X, or a Hölder class As with arbitrary exponent s.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 107, pp. 7–26, 1982. 相似文献
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In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions, expressed in terms of the Carleson constants of related scalar measures. Applications are given to the controllability properties of linear semigroup systems with a Riesz basis of eigenvectors. 相似文献
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Some assertions on free interpolation in spaces of functions analytic in the unit disk with boundary values from the Besov classes B p o (T (1?p<+∞,T is the unit circle) are formulated. 相似文献
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A. G. Lipchinski? 《Siberian Mathematical Journal》2012,53(5):821-838
We consider an interpolation process for the class of functions with finitely many singular points by means of rational functions whose poles coincide with the singular points of the function under interpolation. The interpolation nodes form a triangular matrix. We find necessary and sufficient conditions for the uniform convergence of sequences of interpolation fractions to the function under interpolation on every compact set disjoint from the singular points of the function and other conditions for convergence. We generalize and improve the familiar results on the interpolation of functions with finitely many singular points by rational fractions and of entire functions by polynomials. 相似文献
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S. V. Shvedenko 《Mathematical Notes》1974,15(1):56-61
In this article we study, for a Hilbert spaceB of analytic functions in the open unit disk, the dependence of the structure of the space of sequencesB(Z)={{f(zk)} k=1 ∞ :f∈B} on the choice of the sequence Z={zk} k=1 ∞ of distinct points of the unit disk [6]. 相似文献
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Alain Escassut 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(4):263-280
Let K be an algebraically closed field complete with respect to a dense ultrametric absolute value |.|. Let D be an infraconnected affinoid subset of K and let H(D) be the Banach algebra of analytic elements on D. Let f ∈ H(D) be injective in D and let f * be the mapping defined on the multiplicative spectrum of H(D) that identifies with the set of circular filters on D. We show that f * is injective and maps bijectively the Shilov boundary of H(D) onto this of H(f(D)). Thanks to this property we give a new proof of the equality $\left| {f(x) - f(y)} \right| = \left| {x - y} \right|\sqrt {\left| {f'(x)f'(y)} \right|} $ . 相似文献