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Approksimativnye svoistva nekotorykh mnozhestv v prostranstvakh nepreryvnykh funktsii

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Abstract

Izuchayut·sya approksimativnye svoistva intervalov v prostranstve C(T) nepreryvnykh na kompakte T funktsii. Interval E=[a(t), b(t)] - eto mnozhestvo

$$\{ \varphi \in C(T):a(t) \leqslant \varphi (t) \leqslant b(t),{\text{ }}\forall t \in T\} $$

; a(t) i b(t) - zadannye nepreryvnye funktsii, a(t)≤b(t). Dokazano, chto proksiminal'nyi operator C(T) → E mozhet byt' opredelen tak, chtoby udovletvoryat' uslo-viyu Lipshitsa s konstantoi edinitsa. Poluchen kriterii kompaktnosti intervala. Izuchena zadacha o rasstoyanii mezhdu intervalom i konechnomernym chebyshevskim podprostranstvom i ustanovlena teorema o sil'noi edinstvennosti `ekstremal'nykh `elementov v `etoi zadache. Poluchennye svoistva intervalov primeneny k ustanovleniyu teorem sushchestvovaniya nailuchshego priblizheniya pri approksimatsii funktsii neskol'kikh peremennykh nekotorymi tenzornymi proizvedeniyami.

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  1. Moscow State University of Construction, Yaroslavskoe str. 26, Moscow, 129337, Russia

    S. Ya. Khavinson

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Khavinson, S.Y. Approksimativnye svoistva nekotorykh mnozhestv v prostranstvakh nepreryvnykh funktsii. Analysis Mathematica 29, 87–105 (2003). https://doi.org/10.1023/A:1023948909365

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