On Riemann boundary-value problem for regular functions in Clifford algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 42-56.

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We pose and investigate the Riemann boundary-value problem for regular and strongly regular functions in Clifford alegbras. The posed problem is reduced to the matrix problem for analytical functions in one and two complex variables and we give its solution. We carry out the boundary-value problems in special cases.
Mots-clés : Clifford algebra, regular functions, Riemann boundary-value problem.
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S. P. Kuznetsov; V. V. Mochalov; V. P. Chuev. On Riemann boundary-value problem for regular functions in Clifford algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 42-56. https://geodesic-test.mathdoc.fr/item/IVM_2018_1_a5/

[1] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968

[2] Vekua N. P., Sistemy singulyarnykh integralnykh uravnenii, Nauka, GIFML, M., 1970

[3] Kakichev V. A., Metody resheniya nekotorykh kraevykh zadach dlya analiticheskikh funktsii dvukh kompleksnykh peremennykh, Izd-vo Tyumensk. un-ta, Tyumen, 1978

[4] Simonenko I. B., “K voprosu o razreshimosti bisingulyarnykh i polisingulyarnykh uravnenii”, Funktsion. analiz i ego prilozh., 5:1 (1971), 93–94 | Zbl

[5] Pilidi V. S., “O mnogomernykh bisingulyarnykh operatorakh”, DAN SSSR, 201:4 (1971), 787–789 | Zbl

[6] Bernstein S., “On the left linear Riemann problem in Clifford analysis”, Bull. Belg. Math. Soc., 3:5 (1996), 557–576 | MR | Zbl

[7] Abreu-Blaya R., Bory-Reyes J., Peñ{a} Peñ{a} D., “Jump problem and removable singularities for monogenic functions”, J. Geom. Anal., 17:1 (2007), 1–14 | DOI | MR

[8] Kats B., “On solvability of the jump problem”, J. Math. Anal. Appl., 356:2 (2009), 577–581 | DOI | MR | Zbl

[9] Abreu-Blaya R., Bory-Reyes J., “Criteria for monogenicity of Clifford algebra-valued functions on fractal domains”, Arch. Math. (Basel), 95:1 (2010), 45–51 | DOI | MR | Zbl

[10] Abreu-Blaya R., Bory-Reyes J., Kats B. A., “Approximate dimension applied to criteria for monogenicity on fractal domains”, Bull. Braz. Math. Soc., New Ser., 43:4 (2012), 529–544 | DOI | MR | Zbl

[11] Abreu-Blaya R., Bory-Reyes J., Kats B., “On the solvability of the jump problem in Clifford analysis”, J. Math. Sci. (N. Y.), 189:1 (2013), 1–9 | DOI | MR | Zbl

[12] Kuznetsov S. P., Mochalov V. V., Chuev V. P., “O kraevoi zadache Rimana dlya kvaternionnoznachnykh funktsii”, Matem. modeli i ikh prilozh., 13, Izd-vo Chuvash. un-ta, Cheboksary, 2011, 16–24

[13] Kuznetsov S. P., Mochalov V. V., Chuev V. P., “O kraevoi zadache Rimana dlya kliffordovoznachnykh funktsii v algebre $R_{2,0}$”, Matem. modeli i ikh prilozh., 14, Izd-vo Chuvash. un-ta, Cheboksary, 2012, 28–33

[14] Kuznetsov S. P., Mochalov V. V., Chuev V. P., “O kraevoi zadache Rimana dlya kliffordovoznachnykh funktsii v algebre Pauli”, Matem. modeli i ikh prilozh., 15, Izd-vo Chuvash. un-ta, Cheboksary, 2013, 46–52

[15] Marchuk N. G., Vvedenie v teoriyu algebr Klifforda, Fazis, M., 2012

[16] Kuznetsov S. P., “$B$-mnozhestva v algebrakh Klifforda”, Issledov. po kraevym zadacham i ikh prilozh., Izd-vo Chuvash. un-ta, Cheboksary, 1992, 91–96

[17] Kuznetsov S. P., Mochalov V. V., “Avtomorfizmy algebry Klifforda i silno regulyarnye funktsii”, Izv. vuzov. Matem., 1992, no. 10, 83–86

[18] Kuznetsov S. P., Mochalov V. V., “Predstavlenie operatora Laplasa i silno regulyarnye funktsii v algebrakh Klifforda”, Aktualnye zadachi matem. i mekhan., Izd-vo Chuvash. un-ta, Cheboksary, 1995, 56–70

[19] Kuznetsov S. P., Mochalov V. V., “Struktura nekotorykh klassov regulyarnykh funktsii so znacheniyami v algebre Klifforda”, Izv. Nats. akademii nauk i iskusstv Chuvashskoi Respubliki, 2003, no. 3, 19–29

[20] Kuznetsov S. P., Mochalov V. V., Chuev V. P., “O gruppakh Klifforda i delitelyakh nulya v algebrakh Klifforda”, Vestn. Chuvashsk. un-ta, estestv. i tekhn. nauki, 2015, no. 3, 164–171

[21] Lounesto P., Clifford algebras and spinors, Cambridge Univ. Press, Cambridge, 2011 | MR