On weights which admit the reproducing kernel of Bergman type
نویسندگان
چکیده
منابع مشابه
On Weights Which Admit the Reproducing Kernel of Bergman Type
In this paper we consider (1) the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and (2) the kernels defined by such weights. It is verified that the weighted Bergman kernel has the analogous properties as the classical one. We prove several sufficient conditions and necessary and sufficient conditions for a weight to be...
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Let 1 p 1 and W : R ! (0;1) be continuous. Does W admit a Jackson Theorem in Lp? That is, does there exist a sequence f ng 1 n=1 of positive numbers with limit 0 such that inf deg(P ) n k (f P )W kLp(R) n k f W kLp(R) for all absolutely continuous f with k f 0W kLp(R) nite? We show that such a theorem is true i¤ lim x!1 W 1 Lq [0;x] kWkLp[x;1) = 0; where q is the conjugate parameter of p. In a...
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We study the asymptotic of the Bergman kernel of the spin Dirac operator on high tensor powers of a line bundle.
متن کاملThe Bergman Kernel Function
In this note, we point out that a large family of n × n matrix valued kernel functions defined on the unit disc D ⊆ C, which were constructed recently in [9], behave like the familiar Bergman kernel function on D in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered usi...
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We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the wei...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1992
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171292000012