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Maximal Monotonicity of a Nemytskii Operator

Авторы: Tolstonogov A.A.

Журнал: Functional Analysis and Its Applications

Том: 55

Номер: 3

Год: 2021

Отчётный год: 2022

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DOI: 10.1134/S0016266321030047

Аннотация: A family of maximally monotone operators on a separable Hilbert space is considered. The domains of these operators depend on time ranging over an interval of the real line. The space of square-integrable functions on this interval taking values in the same Hilbert space is also considered. On the space of square-integrable functions a superposition (Nemytskii) operator is constructed based on a family of maximally monotone operators. Under fairly general assumptions, the maximal monotonicity of the Nemytskii operator is proved. This result is applied to the family of maximally monotone operators endowed with a pseudodistance in the sense of A. A. Vladimirov, to the family of subdifferential operators generated by a proper convex lower semicontinuous function depending on time, and to the family of normal cones of a moving closed convex set.

Индексируется WOS: Q4

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Нет

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Индексируется CORE: Нет

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