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In this paper, we obtain new results about the orthogonality measure of orthogonal polynomials on the unit circle, through the study of unitary truncations of the corresponding unitary multiplication operator, and the use of the five-diagonal representation of this operator.Unitary truncations on subspaces with finite co-dimension give information about the derived set of the support of the measure under very general assumptions for the related Schur parameters (an). Among other cases, we study the derived set of the support of the measure when limn|an+1/an|=1, obtaining a natural generalization of the known result for the López class , limn|an|(0,1).On the other hand, unitary truncations on subspaces with finite dimension provide sequences of unitary five-diagonal matrices whose spectra asymptotically approach the support of the measure. This answers a conjecture of L. Golinskii concerning the relation between the support of the measure and the strong limit points of the zeros of the para-orthogonal polynomials.Finally, we use the previous results to discuss the domain of convergence of rational approximants of Carathéodory functions, including the convergence on the unit circle.  相似文献
2.
We consider multidimensional integral operators with bihomogeneous and rotation invariant kernels. For such operators we obtain a criterion for applicability of a projection method in the scalar and matrix cases and describe the limit behavior of the ε-pseudospectra of the truncated operators $A_{\tau _1 , \tau _2 } $ as τ 1 → 0 and τ 2 → 0.  相似文献
3.
We study the limit behavior of the spectral characteristics of truncated multidimensional integral operators whose kernels are homogeneous of degree –n and invariant under the rotation group SO(n). We prove that the limit of the -pseudospectra of the truncated operators K as 0 is equal to the union of the -pseudospectra of the original operator K and the transposed operator .  相似文献
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Let A denote a real linear transformation on Cn which is symmetric and positive-definite relative to the real inner product Rez,w〉, z,wCn. Let FA(Cn) denote the Fock space consisting of holomorphic functions on Cn which are square integrable with respect to the Gaussian measure . For wCn, let , zCn, where KA is the reproducing kernel for FA(Cn). The main aim of this paper is to show that there exist a,b>0 such that the set of functions forms a frame in FA.  相似文献
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In this paper we give direct approximation theorems for a general family of truncated operators. We discuss the linear and nonlinear cases.  相似文献
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We consider the multidimensional integral operators with bihomogeneous kernel invariant under all rotations. For truncated operators of the type we describe the limit behavior of the set of singular values and in the case when these operators are selfadjoint we describe the limit behavior of their spectra.  相似文献
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