Displaying similar documents to “The Fréchet derivative of an analytic function of a bounded operator with some applications.”

Unbounded Hermitian operators and relative reproducing kernel Hilbert space

Palle Jorgensen (2010)

Open Mathematics

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We study unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we identify additional structures that throw light on the problem. We will attack the problem of computing deficiency spaces...

Asymptotic study of canonical correlation analysis: from matrix and analytic approach to operator and tensor approach.

Jeanne Fine (2003)

SORT

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Asymptotic study of canonical correlation analysis gives the opportunity to present the different steps of an asymptotic study and to show the interest of an operator and tensor approach of multidimensional asymptotic statistics rather than the classical, matrix and analytic approach. Using the last approach, Anderson (1999) assumes the random vectors to have a normal distribution and the non zero canonical correlation coefficients to be distinct. The new approach we use, Fine (2000),...

Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase

Frédéric Klopp (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in []. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of []. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues...

Spectral properties of a certain class of Carleman operators

S. M. Bahri (2007)

Archivum Mathematicum

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The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space L 2 X , μ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of A and then using the Stieltjes inversion formula.