Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IVM_2017_2_a2, author = {B. A. Kats}, title = {Riemann boundary-value problem for holomorphic matrices on non-rectifiable curve}, journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika}, pages = {22--33}, publisher = {mathdoc}, number = {2}, year = {2017}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/IVM_2017_2_a2/} }
B. A. Kats. Riemann boundary-value problem for holomorphic matrices on non-rectifiable curve. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 22-33. http://geodesic.mathdoc.fr/item/IVM_2017_2_a2/
[1] Gakhov F. D., “Kraevaya zadacha Rimana dlya sistemy $n$ par funktsii”, UMN, VII:4 (1952), 3–54 | Zbl
[2] Litvinchuk G. S., Spitkovsky I. M., Factorization of measurable matrix functions, Mathematical Research, 37, Akademie Verlag, Berlin, 1987 ; Operator Theory: Advances and Appl., 25, Birkhauser Verlag, Basel–Boston | MR | Zbl | MR | Zbl
[3] Deift P., Orthogonal polynomials and random matrices: a Riemann–Hilbert approach, Courant Lect. Notes, 3, New York Univ., 1999 | MR
[4] Aptekarev A. I., “Matrix Riemann–Hilbert analysis for the case of higher genus—asymptotics of polynomials orthogonal on a system of intervals”, Keldysh Inst. preprints, 2008, 028
[5] Aptekarev A. I., Van Assche W., “Scalar and matrix Riemann–Hilbert approach to the strong asymptotics of Pade approximants and complex orthogonal polynomials with varying weight”, J. Approxim. Theory, 129 (2004), 129–166 | DOI | MR | Zbl
[6] Kats B. A., “The Cauchy transform of certain distributions with application”, Compl. Anal. and Oper. Theor., 6:6 (2012), 1147–1156 | DOI | MR | Zbl
[7] Abreu-Blaya R., Bory-Reyes J., Kats B. A., “Integration over nonrectifiable curves and Riemann boundary value problems”, J. Math. Anal. and Appl., 380:1 (2011), 177–187 | DOI | MR | Zbl
[8] Kats B. A., Kats D. B., “Funktsiya Sege na nespryamlyaemoi duge”, Izv. vuzov. Matem., 2012, no. 4, 12–23
[9] Khërmander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, v. 1, Teoriya raspredelenii i analiz Fure, Mir, M., 1986
[10] Kolmogorov A. N., Tikhomirov V. M., “$\varepsilon$-entropiya i emkost mnozhestv v funktsionalnykh prostranstvakh”, UMN, 14 (1959), 3–86 | MR | Zbl
[11] Falconer K. J., Fractal geometry, 3rd ed., Wiley and Sons, 2014 | MR | Zbl
[12] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977
[13] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1962
[14] Kats B. A., “Kraevaya zadacha Rimana na negladkikh dugakh i fraktalnye razmernosti”, Algebra i analiz, 6:1 (1994), 172–202
[15] Kats B. A., “The Riemann boundary value problem on non-rectifiable curves and related questions”, Complex Variables and Elliptic Equat.: An International J., 59:8 (2014), 1053–1069 | DOI | MR | Zbl
[16] Dolzhenko E. P., “O “stiranii” osobennostei analiticheskikh funktsii”, UMN, 18:4 (1963), 135–142 | MR | Zbl
[17] Nikishin E. M., Sorokin V. N., Ratsionalnye approksimatsii i ortogonalnost, Nauka, M., 1988
[18] Zverovich E. I., “Kraevye zadachi teorii analiticheskikh funktsii v gëlderovskikh klassakh na rimanovykh poverkhnostyakh”, UMN, 26:1 (1971), 113–179 | MR | Zbl