For citation:
Parfilova O. V. On 2-fold completeness of the eigenfunctions for the strongly irregular quadratic pencil of differential operators of second order. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 2, pp. 14-22. DOI: 10.18500/1816-9791-2013-13-2-1-14-22, EDN: SJJAWB
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
27.02.2013
Full text:
(downloads: 134)
Language:
Russian
Heading:
UDC:
517.927.25
EDN:
SJJAWB
On 2-fold completeness of the eigenfunctions for the strongly irregular quadratic pencil of differential operators of second order
Autors:
Parfilova Oksana Vladimirovna, Saratov State Academy of Law
Abstract:
A class of strongly irregular pencils of ordinary differential operators of second order with constant coefficients is considered. The roots of the characteristic equation of the pencils from this class are supposed to lie on a straight line coming through the origin and on the both side of the origin. Exact interval on which the system of eigenfunctions is 2-fold complete in the space of square summable functions is finded.
Key words:
References:
- Shkalikov A. A. Boundary value problems for ordinary differential equations with a parameter in the boundary conditions J. of Math. Sciences, 1986, vol. 33, iss. 6, pp. 1311–1342.
- Rykhlov V. S. On completeness of eigenfunctions of quadratic penciles of ordinary differential operators. Russian Math. [Izv. VUZ. Matematika], 1992, vol. 36, no. 3, pp. 33–42.
- Rykhlov V. S. On properties of eigenfunctions of ordinary differential quadratic pencil of the second order. Integral Transforms and Special Functions. Inform. Byulleten, 2001, vol. 2, no. 1, pp. 85–103 (in Russian).
- Rykhlov V. S. Double completeness of eigenfunctions of a quadratic pencil of second order differential operators. Zbirnik prats’ In-tu matematiki NAN Ukraini, 2009, vol. 6, no. 1, pp. 237–249 (in Russian).
- Rykhlov V. S. O polnote sobstvennykh funktsii differentsial’nogo puchka vtorogo poriadka, korni kharakteristicheskogo uravneniia kotorogo lezhat na odnoi priamoi [On completeness of eigenfunctions of a differential pencil of the second order the roots of the characteristic equation of which lie on a straight line]. Matematika. Mehanika. Saratov, 2007, iss. 9, pp. 88–91 (in Russian).
- Rykhlov V. S. On completeness of eigenfunctions for pencils of differential operators. Spectral and Evolutional Problems : Proc. of the Seventh Crimean Autumn Mathematical School-Symposium. Simferopol, 1997, vol. 7, pp. 70–73 (in Russian).
Received:
24.08.2012
Accepted:
15.01.2013
Published:
27.02.2013
Short text (in English):
(downloads: 66)
- 913 reads