Geodesic
Hilbert problem with unitary coefficient matrix
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 184-191 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the Hilbert problem with unitary matrix-valued coefficient function $G(t)$ a solution is obtained in the form of a series whose general term can be found by quadrature from $G(t)$. Sufficient conditions are determined for the convergence of this series, establishing the dependence of the rate of convergence on the “proximity” of $G(t)$ to the class of matrices of diagonal form, for which the Hilbert problem admits analytic solution in quadratures. The obtained solutions are used to construct the Jost matrix of the coupled $^3S_1+{^3D_1}$ partial channels of $np$ scattering. 
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     author = {V. M. Muzafarov},
     title = {Hilbert problem with unitary coefficient matrix},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {184--191},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a2/}
}
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V. M. Muzafarov. Hilbert problem with unitary coefficient matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 184-191. http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a2/

[1] Vekua N. P., Sistemy singulyarnykh integralnykh uravnenii, Nauka, M., 1970 | MR | Zbl

[2] Newton R. G., J. Math. Phys., 23:12 (1982), 2257–2265 | DOI | MR | Zbl

[3] Gakhov F., Kraevye zadachi, Nauka, M., 1977 | MR

[4] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR

[5] Bogolyubov N. N., Mescheryakov V. A., Tavkhelidze A. N., Tr. simpoziuma po mekhanike sploshnykh sred i problemam analiza, t. I, In-t matematiki AN GSSR, Tbilisi, 1973, 5–14

[6] Gillespie J., Final-state interaction, Holden Day Inc., San Francisco, 1964 | MR

[7] Ferrari E., Riv. Nuovo Cim., 6:2 (1976), 199–216 | DOI | MR

[8] Muzafarov V. M., Troitskii V. E., Trubnikov S. V., EChAYa, 14:5 (1983), 1112–1145

[9] Nyuton R., Teoriya rasseyaniya voln i chastits, Mir, M., 1969 | MR

[10] Reiner M. J., Phys. Rev. Lett., 32:2 (1974), 236–240 ; Reiner M. J., Ann. of Phys., 100:1/2 (1976), 131–191 | DOI | DOI

[11] Newton R. G., Fulton T., Phys. Rev., 107:7 (1957), 1103–1119 | DOI

[12] Meunargiya O. V., TMF, 37:3 (1978), 423–426 | MR | Zbl

[13] Kharakhan M. L., Shirokov Yu. M., TMF, 3:1 (1970), 100–105

[14] Troitskii V. E., TMF, 37:2 (1978), 243–245 | MR

[15] Budnev V. M., Serebryakov V. V., YaF, 23:6 (1976), 1306–1315

[16] Muzafarov V. M., YaF, 27:6 (1978), 1686–1693 | MR

[17] Bessis D., Turchetti G., Nucl. Phys., B123:1 (1977), 173–189 | DOI

[18] Turchetti G., Fortschr. Phys., 26:1 (1978), 1–27 | DOI | MR

[19] Muzafarov V. M., Avtoref. dis. na soiskanie uch. st. kand. fiz.-matem. nauk, MIAN SSSR, M., 1980

[20] Arndt R. A. et al., Phys. Rev., D28:1 (1983), 97–122