Inversion of potential-type operators with symbols degenerate on hyperboloids and paraboloids
Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 814-824.

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The method of approximative inverse operators is applied to the inversion of certain potential-type operators with symbols degenerate on hyperboloids or paraboloids. Using this method, the inversion is constructed as the limit of a sequence of convolutions with summable kernels that are expressed in terms of elementary or special functions.
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D. V. Vozhzhov; V. A. Nogin. Inversion of potential-type operators with symbols degenerate on hyperboloids and paraboloids. Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 814-824. http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a1/

[1] S. G. Samko, “Hypersingular integrals and their applications”, Analytical Methods and Special Functions, 5, Taylor Francis, London–New York, 2002, 358–373 | MR | Zbl

[2] V. A. Nogin, S. G. Samko, “Some applications of potentials and approximative inverse operators in multi-dimensional fractional calculus”, Fract. Calc. Appl. Anal., 2:2 (1999), 205–228 | MR | Zbl

[3] V. A. Nogin, S. G. Samko, “Method of approximating inverse operators and its applications to the inversion of potential-type integral transforms”, Integral Transform. Spec. Funct., 8:1–2 (1999), 89–104 | DOI | MR | Zbl

[4] M. M. Zavolzhenskii, V. A. Nogin, “Approksimativnyi podkhod k obrascheniyu obobschennykh potentsialov Rissa”, Dokl. RAN, 324:4 (1992), 738–741 | MR | Zbl

[5] E. D. Alisultanova, V. A. Nogin, Obraschenie nekotorykh potentsialov Rissa s simvolami, lineino vyrozhdayuschimisya na giperploskosti, Dep. v VINITI, No 2271-V91, VINITI, Rostov-na-Donu, 1991

[6] E. D. Alisultanova, V. A. Nogin, “Obraschenie i opisanie obobschennogo potentsiala Rissa s kvadratichnymi kharakteristikami”, Izv. vuzov. Matem., 1993, no. 2, 3–11 | MR | Zbl

[7] S. G. Samko, Gipersingulyarnye integraly i ikh prilozheniya, Izd-vo Rostovskogo un-ta, Rostov-na-Donu, 1984 | MR | Zbl

[8] B. Rubin, “Hypersingular integrals of Marchaud type and the inversion problem for potentials”, Math. Nachr., 165 (1994), 245–321 | DOI | MR | Zbl

[9] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Spetsialnye funktsii, Nauka, M., 1983 | MR | Zbl

[10] I. M. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR | Zbl

[11] S. L. Sobolev, “Ob odnoi teoreme funktsionalnogo analiza”, Matem. sb., 4:3 (1938), 471–497 | Zbl

[12] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, t. 1, Nauka, M., 1973 | MR | Zbl