Integral equations of the form (2) below, dual to (1) are studied from the point of view of finding their effective solutions, the results being given in Section 1. The results are applied in Section 2 for solving nonlocal problems for the polyharmonic functions in the half plane.
@article{bwmeta1.element.bwnjournal-article-bcpv37i1p251bwm,
author = {Obolashvili, Elena},
title = {Effective solutions of some dual integral equations and their applications},
journal = {Banach Center Publications},
volume = {37},
year = {1996},
pages = {251-257},
zbl = {0881.45002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p251bwm}
}
Obolashvili, Elena. Effective solutions of some dual integral equations and their applications. Banach Center Publications, Tome 37 (1996) pp. 251-257. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p251bwm/
[000] [1] V. I. Azamatova, Integral equations with the difference and summary kerns in the space (α,β), Izv. AN BSSR Phys. Math. No. 5 (1972), 24-33 (Russian).
[001] [2] F. D. Berkovic, An integral equation on the semi-axis, Izv. Vyssh. Uchebn. Zaved. Mathem. 1966 no. 1 (50), 3-14. (Russian).
[002] [3] F. D. Gakhov, U. I. Cherski, Equations of convolution type, (Russian), 'Nauka', Moscow, 1978.
[003] [4] N. I. Muskhelishvili, Singular integral equations, Groningen, Noordhoff, 1963.
[004] [5a] E. I. Obolashvili, Nonlocal problems for some partial differential equations, Applicable Analysis, vol. 45, 1992, 269-280. | Zbl 0771.35012
[005] [5b] E. I. Obolashvili, Nonlocal problems for the Beltrami Equation and Polyharmonic Functions, Proceedings devoted to N. I. Muskhelishvili's anniversary, Tbilisi 1994.
[006] [6] V. V. Sobolev, Diffuse irradiation in a medium with mirror reflection boundaries, DAN SSSR 136 (1961) 571-574 (Russian). | Zbl 0103.23202
[007] [7] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford 1950. | Zbl 0017.40404