On Multiple Completeness of the Root Functions of a Certain Class of Pencils of Differential Operators with Constant Coefficients

Victor S. Rykhlov

Abstract


We consider the class of pencils of the -th order ordinary differential operators with constant coefficients. It is assumed that the roots of the characteristic equation of pencils from this class are simple, non-zero and located arbitrarily in the complex plane. Sufficient conditions are formulated for -fold completeness () of the system of root functions of the pencils from this class in the space of summable with square functions on the main segment.


Volltext:

PDF (Russian)

Literaturhinweise


Freiling G. Zur Vollständigkeit des Systems der Eigenfunktionen und Hauptfunktionen irregulärer Operator-büschel: Math. Z. 1984, Vol. 188, №. 1; 55–68.

Freiling G. Über die mehrfache Vollständigkeit des Systems der Eigenfunktionen und assoziierten Funktionen irregulärer Operatorenbüschel in : ZAMM. 1985. Vol. 65, № 5; 336 – 338.

Keldysh MV. On eigenvalues and eigenfunctions of some classes of non-selfadjoint equations: Dokl. AN SSSR. 1951, Vol. 77, №1; 11 – 14. (in Russian).

Khromov A P. Finite-dimensional perturbations of Volterra operators: Dr. phys. and mat. sci. diss. Novosibirsk, 1973,242. (in Russian).

Rykhlov V S. Multiple completeness of the eigenfunctions of an ordinary differential polynomial pencil: Issledovaniya po teorii operatorov: Sb. Statei. Ufa: BNC UrO AN SSSR, 1988; 128–140.

Rykhlov V S, Blinkova OV. On multiple completeness of the root functions of a certain class of pencils of differential operators with constant coefficients: Izv. Sar. Univ. N.S. Ser. Math. Mech. Inform. 2014, Vol. 14, Iss. 4. Part. 2, 574–584.

Shkalikov AA. On completeness of eigenfunctions and associated function of an ordinary differential operator with separated irregular boundary conditions, Funktsional. Anal. i Prilozhen. 1976, Vol. 10, №4; 69–80.(in Russian).

Shkalikov AA. Boundary value problems for ordinary differential equations with a parameter in the boundary conditions: J. Soviet Math. 1986, Vol. 33, Iss. 6;1311 – 1342.

Vagabov AI. Introduction to spectral theory of differential operators, Rostov-na-Donu: Izd-vo Rost. un-ta, 1994;160. (in Russian).


Refbacks