Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


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

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
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Russian
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517.927.25

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. 

References: 
  1. 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.
  2. 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.
  3. 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).
  4. 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).
  5. 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).
  6. 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).
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