Criteria for the unconditional basis property and the Riesz basis property for a system of root functions of an ordinary nonselfadjoint 2m-order differential operator (which are understood in a framework developed by V. A. Il'in, i.e. irrespective of boundary conditions) were established. The criterion for Bessel property in $L_2$ of such systems also was established. As an instrument of researching, a subdivision of a root function system onto classes in terms of relations between there norms in different spaces was proposed. It has been proved that one can modify any system of root functions by means of linear combinations (with eigenfunctions remained valid) so that new system satisfies a posteriory estimation. For extended systems of sines, cosines, exponentials and systems of root functions of 2-order operator, it has been proved that the Bessel and Hilbert properties are stable with respect to small perturbations of spectral parameter.
Main publications:
Budaev V. D. O neravenstve Besselya dlya sistem kornevykh funktsii differentsialnykh operatorov // Doklady AN SSSR, 1991, 318(1), 16–20.
Budaev V. D. Neobkhodimoe uslovie bazisnosti Rissa sistem kornevykh obyknovennogo nesamosopryazhennogo differentsialnogo operatora // Differentsialnye uravneniya, 1993, 29(1), 20–30.
Budaev V. D. Nekotorye svoistva kornevykh funktsii differentsialnykh operatorov, svyazannye s bezuslovnoi bazisnostyu // Differentsialnye uravneniya, 1996, 32(1), 9–14.
Budaev V. D. O neravenstvakh Gilberta i Besselya dlya nekotorykh sistem funktsii // Doklady Akademii nauk, 1997, 357(2), 157–160.
