Published April 24, 2023
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ON THE SPECTRUM OF A SECOND ORDER LINEAR INTEGRO-DIFFERENTIAL OPERATOR ON THE SEMI-AIS
Authors/Creators
- 1. professor, doctor of Mathematical Sciences Azerbaijan State University of Economics (UNEC)
Description
We prove that subject to the conditions the eigen-values of the integro-differential (i.e.) operator form a bounded finite or denumerable set whose limit points can be located only on the positive semi-axis.
It is shown that subject to the conditions of the form
the number of eigen-values of form a finite set.
In the paper it is shown the boundary of the domain in the complex plane outside which knowingly there is no spectrum of the integro-differential operator . And it is also proved that if belongs to the spectrum, then the resolvent of the integro-differential operator is a bounded integral operator with the kernel , satisfying the conditions
Notes
References:
1. Naimark M.A. Linear differential operators. Nauka, Moscow, 1969, p.24-50.
2. Naimark M.A. Studying spectrum and expansion in eigen functions of a
second order not self-adjoint differential operator on a semi-axis. Trudy Moskovskoqo Matematicheskogo Obshestva, №3, 1954, p.181-270.
3. Levitan B.M., Sargsyan I.S. Introduction to spectral theory Nauka, Moscow 1970, 254-304.
4. Achiezer N.I. Glazman I.M. Theory of linear operators in Hilbert spaces. Nauka 1966, 316-348, 438-467.
5. Sansone J. Ordinary differential equations. I-IL, 1953.
6. Almmadov M.S. On eigen-values and particular solutions of a second order linear inregro-differential operator. Annali d'Izalia N:38/2022 78-83. ISSN 3572-2436
7. M.S Almamedov, On a spectrum of a fourth-order linear integro-differential operator, Dokl. Akad. Nauk SSSR, 299:3 (1988), 525–529; Dokl. Math., 37:2 (1988), 385–389
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