On delta-extension for a Noether operator
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 40-53.

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We examine a third kind integral equation in the class of generalized functions. We show that the considered equation has similar solvability properties as the Fredholm equation of the second kind.
Keywords: integral equation of the third kind, characteristic numbers, fundamental functions, singular operator.
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E. Tompé Weimbapou; Abdourahman; E. Kengne. On delta-extension for a Noether operator. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 40-53. http://geodesic.mathdoc.fr/item/IVM_2021_11_a4/

[1] Ferziger J. H., Kaper H. G., Mathematical Theory of Transport Processes in Gases, North-Holland Publ. compagny, Amsterdam–London, 1972

[2] Hilbert D., Grundzüge einer allgemeinen Theorie der linear Integralgleichungen, Chelsea Publ. Company, New York, 1953

[3] Picard E., “Un théorème général sur certaines équations intégrales de troisième espèce”, Comptes Rendus, 150 (1910), 489–491 | Zbl

[4] Bart G. R., “Three theorems on third kind linear integral equations”, J. Math. Anal. and Appl., 79 (1981), 48–57 | DOI | Zbl

[5] Bart G. R., Warnock R. L., “Linear integral equations of the third kind”, SIAM J. Math. Anal., 4 (1973), 609–622 | DOI | Zbl

[6] Sukavanam N., “A Fredholm-Type theory for third kind linear integral equations”, J. Math. Anal. and Appl., 100 (1984), 478–484 | DOI

[7] Shulaia D., “On one Fredholm integral equation of third kind”, Georgian Math. J., 4 (1997), 464–476 | DOI

[8] Shulaia D., “Solution of a linear integral equation of third kind”, Georgian Math. J., 9 (2002), 179–196 | DOI | Zbl

[9] Shulaia D., “Integral equations of third kind for the case of piecewise monotone coefficients”, Transactions of A. Razmadze Math. Institute, 171 (2017), 396–410 | DOI | Zbl

[10] Rogozhin V. S., Raslambekov S. N., “Noether theory of integral equations of the third kind in the space of continuous and generalized functions”, Soviet Math. (Iz. VUZ), 23:1 (1979), 48–53 | Zbl

[11] Abdourahman A., On a linear integral equation of the third kind with a singular differential operator in the main part, Deponierted in VINITI, Moscow, 28.03.2002, No 560-B2002, VINITI, Rostov-na-Donu, 2002

[12] Abdourahman A., Karapetiants N., “Noether theory for third kind linear integral equation with a singular linear differential operator in the main part”, Proceedings of A. Razmadze Math. Institute, 135 (2004), 1–26 | Zbl

[13] Gabbassov N. S., On direct methods of the solutions of Fredholm's integral equations in the space of generalized functions, PhD thesis, Kazan, 1987

[14] Gabbasov N. S., “Methods for Solving an Integral Equation of the Third Kind with Fixed Singularities in the Kernel”, Diff. Equat., 45 (2009), 1341–1348 | DOI | Zbl

[15] Gabbasov N. S., “A Special Version of the Collocation Method for Integral Equations of the Third Kind”, Diff. Uravn., 41 (2005), 1690–1695 | Zbl

[16] Gabbasov N. S., Methods for Solving Fredholm Integral Equations in Spaces of Distributions, Kazan, 2006

[17] Karapetiants N. S., Samko S. G., Equations with Involutive Operators, Birkhauser, Boston–Basel–Berlin, 2001 | Zbl

[18] Prossdorf S., Some classes of singular equations, Mir, M., 1979 (in Russian) | Zbl

[19] Bart G. R., Warnock R. L., “Solutions of a nonlinear integral equation for high energy scattering. III. Analyticity of solutions in a parameter explored numerically”, J. Math. Phys., 13 (1972), 1896–1902 | DOI

[20] Bart G. R., Johnson P. W., Warnock R. L.,, “Continuum ambiguity in the construction of unitary analytic amplitudes from fixed-energy scattering data”, J. Math. Phys., 14 (1973), 1558–1565 | DOI