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On the theory differential realization: Criterion for the continuity of the nonlinear Rayleigh-Ritz operator

Авторы: Rusanov V.A., Daneev A.V., Lakeyev A.V., Linke Yu.É.

Журнал: International Journal of Functional Analysis, Operator Theory and Applications

Том: 12

Номер: 1

Год: 2020

Отчётный год: 2020

Издательство:

Местоположение издательства:

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DOI: 10.17654/FA012010001

Аннотация: The paper considers a nonlinear functional Rayleigh-Ritz operator defined on a set of pairs of measurable functions. It is equal to the ratio of their moduli, when the denominator is nonzero, and to zero in the opposite case. Continuity of this operator with respect to convergence and also with respect to the measure is investigated. It has been demonstrated that convergence of the operator’s value on the sequence of pairs to the value on the limit pair of functions necessitates not only convergence with respect to the measure of its arguments but also convergence with respect to the measure of carriers of the second argument to the carrier of its limit. The results obtained may be applied in the theory of differential realization (in the Hilbert space) of nonlinear dynamic models of higher orders.

Индексируется WOS: Нет

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Нет

Индексируется ВАК: Нет

Индексируется CORE: Нет

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