Conservative Realizations of Herglotz-Nevanlinna Functions

Arlinskii, Yuri; Belyi, Sergey; Tsekanovskiı̆, Eduard

doi:10.1007/978-3-7643-9996-2

Cited by 46 publications

(41 citation statements)

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“…In the case of a nondensely defined nonnegative symmetric operator A, characterizations of its Friedrichs extension A F and its Kreȋn extension A K can be found in [7,26], a description of its generalized resolvents of the class C .A/ was given in [35]. For descriptions of maximal accretive and maximal sectorial extensions of sectorial and, in particular, nonnegative operators see surviews [8][9][10] and references therein.…”

Section: Definition 14mentioning

confidence: 98%

Boundary Triplets, Weyl Functions, and the Kreĭn Formula

Derkach

2015

Operator Theory

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Section: Definition 14mentioning

confidence: 98%

Boundary Triplets, Weyl Functions, and the Kreĭn Formula

Derkach

2015

Operator Theory

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“…This exposition does not cover other methods in the theory of generalized resolvents developed in [65] (see in this concern recent surviews [8,10]). …”

Section: Generalized Resolvents Of Nonnegative Operatorsmentioning

confidence: 99%

“…For descriptions of maximal accretive and maximal sectorial extensions of sectorial and, in particular, nonnegative operators see surviews [8][9][10] and references therein.…”

Section: Definition 14mentioning

confidence: 99%

Boundary Triplets, Weyl Functions, and the Kreĭn Formula

Derkach

2014

Operator Theory

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This chapter contains a short review of the theory of boundary triplets, and the corresponding Weyl functions, of symmetric operators in Hilbert and Kreȋn spaces. The theory of generalized resolvents of such operators is exposed from the point of view of boundary triplets approach. Applications to different continuation problems related to the extension theory of Kreȋn space symmetric operators are discussed.

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“…In the scalar case, the corresponding classes were carefully studied by Kats/Krein [17] and Krein/Nudelman [19,Appendix]. What concerns the treatment of several matricial and operatorial generalizations, we refer the reader to the monograph Arlinskii/Belyi/Tsekanovskii [1] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On Matrix-valued Stieltjes Functions with an Emphasis on Particular Subclasses

Fritzsche

Kirstein

Mädler

2017

Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics

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Dedicated to our friend and colleague Albrecht Böttcher on the occasion of his 60th birthdayThe paper deals with particular classes of q × q matrix-valued functions which are holomorphic in C \ [α, +∞), where α is an arbitrary real number. These classes are generalizations of classes of holomorphic complex-valued functions studied by Kats and Krein [17] and by Krein and Nudelman [19]. The functions are closely related to truncated matricial Stieltjes problems on the interval [α, +∞). Characterizations of these classes via integral representations are presented. Particular emphasis is placed on the discussion of the Moore-Penrose inverse of these matrix-valued functions.

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Conservative Realizations of Herglotz-Nevanlinna Functions

Cited by 46 publications

References 0 publications

Boundary Triplets, Weyl Functions, and the Kreĭn Formula

Boundary Triplets, Weyl Functions, and the Kreĭn Formula

Boundary Triplets, Weyl Functions, and the Kreĭn Formula

On Matrix-valued Stieltjes Functions with an Emphasis on Particular Subclasses

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