O predstavlenii lineinykh operatorov, perestanovochnykh s operatorom umnozheniya |
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| Authors: | Yu. F. Korobeinik |
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| Affiliation: | (1) Rostov State University, Faculty of Mathematics and Mechanics, Rostov-na-Donu 344090, ul. Zorge 5, Russia |
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| Abstract: | Summary Pust' Ej (j =1,2) - lokal'no vypuklye prostranstva funktsii, odnoznachnykh i lokal'no analiticheskikh na nekotorom mnozhestve Q ⊂ℂ. Pust', dalee, m(E1,E2) - mnozhestvo vsekh mul'tiplikatorov pary E1, E2 i L (E1, E2) sovokupnost' vsekh lineinykh operatorov, deistvuyushchikh iz E1 v E2. V stat'e e pri opredelennykh predpolozheniyakh poluchen kriterii predstavleniya operatora T iz L (E1, E2), kommutiruyushchego s fiksirovannym elementom a∊ m(E1,E1) ∩m(E2,E2), v kanonicheskoi forme Ty = b · y, gde b∊m(E1,E2). Obsuzhdayut·sya predpolozheniya, pri kotorykh poluchen kriterii, i privodyat·sya primery, pokazyvayushchie ikh sushchestvennost'. |
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