Hilbert spaces related to harmonic functions
نویسندگان
چکیده
منابع مشابه
Reproducing Kernels for Hilbert Spaces of Real Harmonic Functions
This paper studies a family of Hilbert spaces of real harmonic functions on bounded regions in Rn and will show that, for a range of values of s, they are reproducing kernel Hilbert spaces. The spaces are characterized by their boundary traces and the inner products are defined via their expansions in the harmonic Steklov eigenfunctions of the region. The reproducing kernels will then be descri...
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1. Introduction. The research reported on in the present note was motivated by the following Proposition (F), due to Ernest Fischer ([5], see also [4] for an earlier version; actually Fischer proved a more general result, but the special case suffices as a point of departure for our discussion) : (F) Let P denote a homogeneous polynomial in si, • • • , z k with complex coefficients. Then every ...
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Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also present some computational properties and examples.
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in this paper, we considered composition operators on weighted hilbert spaces of analytic functions and observed that a formula for the essential norm, gives a hilbert-schmidt characterization and characterizes the membership in schatten-class for these operators. also, closed range composition operators are investigated.
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1996
ISSN: 0040-8735
DOI: 10.2748/tmj/1178225416