Certain Hilbert Spaces of Entire Functions
نویسنده
چکیده
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 polynomial in Si, • • • , z k has a unique representation QP+R where
منابع مشابه
Error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion
On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.
متن کاملComposition operators acting on weighted Hilbert spaces of analytic functions
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.
متن کاملPolarization constant $mathcal{K}(n,X)=1$ for entire functions of exponential type
In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have t...
متن کاملOn the expansion theorem described by H(A, B) spaces
The aim of this paper is to construct a generalized Fourier analysis for certain Hermitian operators. When A, B are entire functions, then H(A,B) will be the associated reproducing kernel Hilbert spaces of Cn×n-valued functions. In that case, we will construct the expansion theorem forH(A,B) in a comprehensive manner. The spectral functions for the reproducing kernel Hilbert spaces will also be...
متن کامل$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework
In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...
متن کاملSupercyclic tuples of the adjoint weighted composition operators on Hilbert spaces
We give some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(C_{omega_1,varphi_1}^* , C_{omega_2,varphi_2}^*)$ on the Hilbert space $mathcal{H}$ of analytic functions is supercyclic.
متن کامل