caa a22 4500 606200886 CHVBK 20210128100945.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00025-015-0450-6 doi (NATIONALLICENCE)springer-10.1007/s00025-015-0450-6 Rykhlov Victor Saratov State University, 83 Astrakhanskaya Street, 410012, Saratov, Russia aut Multiple Completeness of the Root Functions for a Certain Class of Pencils of Ordinary Differential Operators with Constant Coefficients [Elektronische Daten] [Victor Rykhlov] A class of polynomial pencils of ordinary differential operators with constant coefficients is considered in the article. The pencils from this class are generated by the n-th order ordinary differential expression and two-point boundary conditions. Coefficients of the differential expression are supposed to be polynomials of the spectral parameter with constant coefficients. The boundary conditions are supposed to depend on the spectral parameter polynomially. It is assumed that the roots of the characteristic equation of the pencils from this class are simple, non-zero and lie on two rays emanating from the origin. The author investigates n-fold completeness of the root functions of the pencils from this class in the space of summable with square functions on the main segment. Sufficient conditions of the n-fold completeness of the root functions are obtained. The main idea of the method of the proof of the theorem is a new asymptotics of the characteristic determinant of the pencil. The presented results supplement previous results of the author. Springer Basel, 2015 Pencil of ordinary differential operators nationallicence root functions nationallicence multiple completeness nationallicence polynomial pencil of operators nationallicence system of root functions nationallicence eigenfunctions nationallicence associated functions nationallicence Results in Mathematics Springer Basel 68/3-4(2015-11-01), 427-440 1422-6383 68:3-4<427 2015 68 25 https://doi.org/10.1007/s00025-015-0450-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-015-0450-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rykhlov Victor Saratov State University, 83 Astrakhanskaya Street, 410012, Saratov, Russia aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 68/3-4(2015-11-01), 427-440 1422-6383 68:3-4<427 2015 68 25