On Indefinite Moment Problems and Resolvent Matrices of Hermitian Operators in Kreîn Spaces | Zendy

Derkach Vladimir | Zendy

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On Indefinite Moment Problems and Resolvent Matrices of Hermitian Operators in Kreîn Spaces

Author(s) -

Derkach Vladimir

Publication year - 1997

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19971840106

Subject(s) - mathematics , hermitian matrix , resolvent , moment problem , eigenvalues and eigenvectors , pure mathematics , matrix (chemical analysis) , moment (physics) , self adjoint operator , simple (philosophy) , mathematical analysis , hilbert space , algebra over a field , philosophy , statistics , physics , materials science , epistemology , classical mechanics , quantum mechanics , principle of maximum entropy , composite material

Let ( s j )∞ j =0 be a sequence of real numbers such that the Hankel matrices ( s i+j )∞ 0 , ( S i+j+i )∞ 0 have finite numbers of negative eigenvalues. The indefinite moment problem with the moments S j (j = 0,1,2, …) and the corresponding Stieltjes string are investigated. We use the approach via the Kreîn — Langer extension theory of symmetric operators in spaces with indefinite metric. In the framework of this approach a description of L– resolvents of a class of symmetric operators in Kreîn space and a simple formula for the calculation of the L– resolvent matrix in terms of boundary operators are given.

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