On Classes of Stieltjes Type Operator-Valued Functions with Gaps | Zendy

Vladislavi Eduardovic Tsekanovskii | Zendy

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On Classes of Stieltjes Type Operator-Valued Functions with Gaps

Author(s) -

Vladislavi Eduardovic Tsekanovskii

Publication year - 1992

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/614

Subject(s) - riemann–stieltjes integral , type (biology) , mathematics , operator (biology) , pure mathematics , algebra over a field , mathematical analysis , chemistry , geology , paleontology , biochemistry , repressor , transcription factor , integral equation , gene

Classes of Stieltjes type operator-valued functions with gaps on the positive semi-axis (i.e., with intervals of holomorphy and definiteness) are considered. We prove criteria that a given function, whose values are operators in a finite-dimensional Hubert space, belongs to these classes. Moreover, we investigate classes of Stieltjes type operator-valued functions which admit a realization, i.e., which can be represented as fractional linear transformations of operator-valued transfer functions of conservative scattering systems of the form

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