Geodesic
Vector transformation operators for harmonic functions in a ball
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2010), pp. 48-56

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The operator $L_\Gamma $ and the inverse operator $L_\Gamma ^{-1} $ are investigated; they are used at finding transformation operators and at the solution of concrete boundary value problems in homogeneous spherically symmetric areas. The operational solution method of vector boundary value problems is offered. In particular, the solution of the third boundary value problem in ball for the Laplace equation is found.
Keywords: transformation operator, vector boundary value problems, harmonic functions. 
Yu. A. Parfenova. Vector transformation operators for harmonic functions in a ball. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2010), pp. 48-56. http://geodesic.mathdoc.fr/item/VSGU_2010_2_a4/
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     title = {Vector transformation operators for harmonic functions in a~ball},
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[1] Gobson E. V., Teoriya sfericheskikh i ellipsoidalnykh funktsii, Inostr. lit., M., 1952, 476 pp.

[2] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Nauka, M., 1970, 800 pp.

[3] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966, 575 pp. | MR

[4] Bavrin I. I., Operatornyi metod v kompleksnom analize, Prometei, M., 1991, 200 pp. | MR | Zbl

[5] Bavrin I. I., Yaremko O. E., “Operatory preobrazovaniya i kraevye zadachi teorii garmonicheskikh i bigarmonicheskikh funktsii”, Doklady RAN, 393:4 (2003), 439–444 | MR

[6] Koshlyakov N. S., Gliner E. B., Smirnov M. M., Uravneniya v chastnykh proizvodnykh matematicheskoi fiziki, Vysshaya shkola, M., 1970, 710 pp. | Zbl