Published April 12, 2023 | Version v1

EXPANSİON OF THE GREEN FUNCTİON OF İNTEGRO-DİFFERENTİAL OPERATOR

Authors/Creators

  • 1. professor, doctor of Mathematical Sciences Azerbaijan State University of Economics (UNEC)

Description

Abstract

For obtaining formulas of expansions of the integro-differential operator  in eigen-functions, at first we consider a boundary value problem in the finite interval , write formulas of expansions in eigen-functions and then tending   we obtain expansion for the integro-differential operator .

To obtain expansion of the Green function  of the integro-differential operator  we will assume that

  1. the conditions  are fulfilled .
  2.  does not vanish at the points of the real axis
  3. the zeros  are simple.

Notes

References: 1. Naimark M.A. Studying spectrum and expansion of a second order not self-adjoint differential operator in eigen functions on a semi-axis. Trudy Moskovskoqo Matematicheskogo Obshestva, №3, 1954, p.181-270. 2. Naimark M.A. Linear differential operators. Nauka, Moscow, 1969, p.24-50. 3. Naimark M.A. Spectral analysis of not self-adjoint operators. UMN, 11, 6(72), 1956, p.183-202. 4. Pavlov B.S. On self adjoint operator on a semi-axis. DAN SSSR, 141, 4(1961), p.807-810. 5. Sansone J. Ordinary differential equations. İ-Il, 1953. 6. Almammadov M.S. On eigen-values and particular solutions of a second order linear integro-differential operator. Annali d'Italia, #38/2022, sn. 78-83 ISSN 3572-2436 7. Almammadov M.S. On the spectrum of a fourth order linear integro-differential operator. Doklady AN SSSR, v.29, №3, 1988, p.525-529.

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