Spektral'naya Teoriya Differentsial'nykh Operatorov

V nastoyashchey rabote vyyavleny prostye i sushchestvennye algebraicheskie kriterii kratnoy polnoty kornevykh funktsiy kraevykh zadach dlya lineynykh puchkov ODU, a takzhe kratnoy razlozhimosti po nim proizvol'nykh funktsiy. V izlozhenii predlagayutsya ryad novykh teorem, vnosyashchikh v teoriyu estestvennuyu zavershennost'. Dlya obshchikh sistem lineynykh obyknovennykh differentsial'nykh uravneniy s kompleksnym parametrom , pri predel'no slabykh ogranicheniyakh gladkosti koeffitsientov, ustanovleno sushchestvovanie eksponentsial'no asimptoticheskikh po matrichnykh resheniy. Poluchennye resheniya ispol'zovany v issledovanii regulyarnosti po G. Birkgofu puchkov obyknovennykh differentsial'nykh operatorov (n-kratnoy razlozhimosti n proizvol'nykh funktsiy po kornevym funktsiyam puchka). Privedeny geometricheski prozrachnye usloviya regulyarnosti, blizkie k kriteriyam i obobshchayushchie izvestnye chastnye sluchai (usloviya Shturma, Birkgofa, Tamarkina, periodicheskie usloviya i dr.). Rabota rasschitana na shirokiy krug chitateley, imeyushchikh otnoshenie k voprosam spektral'noy teorii differentsial'nykh operatorov.