Reproducing kernels , Bergman kernels , Poisson kernels
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چکیده
منابع مشابه
HILBERT SPACES OF TENSOR-VALUED HOLOMORPHIC FUNCTIONS ON THE UNIT BALL OF Cn
The expansion of reproducing kernels of Bergman spaces of holomorphic functions on a domain D in Cn is of considerable interests. If the domain admits an action of a compact group K, then naturally one would like to decompose the space of polynomials into irreducible subspaces of K and expand the reproducing kernels in terms of the reproducing kernels of the finite dimensional subspaces. In [5]...
متن کاملToeplitz Operators and Weighted Bergman Kernels
For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman...
متن کاملSome Properties of Reproducing Kernel Banach and Hilbert Spaces
This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...
متن کاملHUA OPERATORS ON BOUNDED HOMOGENEOUS DOMAINS IN C n AND ALTERNATIVE REPRODUCING KERNELS FOR HOLOMORPHIC FUNCTIONS
(1) Contain all real and imaginary parts of bounded holomorphic functions. (2) Be describable as \Poisson integrals" over the Bergman-Shilov boundary against a real kernel (the \Poisson" kernel). (3) Be invariant under all bi-holomorphisms of the domain. (4) Be describable as the nullspace HL of a degenerate-elliptic system L of second order di erential operators. (We refer to HL as the space o...
متن کاملBerezin Transforms on Pluriharmonic Bergman Spaces
We show that, perhaps surprisingly, in several aspects the behaviour of the reproducing kernels, of Toeplitz operators and of the Berezin transform on some weighted pluriharmonic Bergman spaces is the same as in the holomorphic case.
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