Geodesic
Factorization of matrices depending on a parameter, and elliptic equations in a halfspace
Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 65-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we prove the theorem that every matrix-function on the circle depending on a parameter admits a triangular factorization which is continuous in the parameter. Using this theorem, we manage to construct explicitly a regularizer of the boundary value problem for an elliptic system of pseudo-differential equations in a halfspace. Figures: 8. Bibliography: 16 titles. 
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M. A. Shubin. Factorization of matrices depending on a parameter, and elliptic equations in a halfspace. Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 65-84. http://geodesic.mathdoc.fr/item/SM_1971_14_1_a3/

[1] M. S. Budyanu, I. Ts. Gokhberg, “Obschie teoremy o faktorizatsii matrits-funktsii. I. Osnovnaya teorema”, Matem. issledovaniya, III:2 (1968), 87–103

[2] M. I. Vishik, G. I. Eskin, “Uravneniya v svertkakh v ogranichennoi oblasti”, Uspekhi matem. nauk, XX:3(123) (1965), 89–152

[3] M. I. Vishik, G. I. Eskin, “Ellipticheskie uravneniya v svertkakh v ogranichennoi oblasti”, Uspekhi matem. nauk, XXII:1(133) (1967), 15–76

[4] M. I. Vishik, G. I. Eskin, “Normalno razreshimye zadachi dlya ellipticheskikh sistem uravnenii v svertkakh”, Matem. sb., 74(116) (1967), 326–356 | MR | Zbl

[5] I. Ts. Gokhberg, “Zadacha faktorizatsii v normirovannykh koltsakh, funktsii ot izometricheskikh i simmetricheskikh operatorov i singulyarnye integralnye uravneniya”, Uspekhi matem. nauk, XIX:1(115) (1964), 71–124

[6] I. Ts. Gokhberg, M. G. Krein, “Osnovnye polozheniya o defektnykh chislakh, kornevykh chislakh i indeksakh lineinykh operatorov”, Uspekhi matem. nauk, XII:2(74) (1957), 43–118

[7] I. Ts. Gokhberg, M. G. Krein, “Sistemy integralnykh uravnenii na poluosi s yadrami, zavisyaschimi ot raznosti argumentov”, Uspekhi matem. nauk, XIII:2(80) (1958), 3–72

[8] I. F. Donin, “O deformatsiyakh golomorfnykh vektornykh rassloenii nad sferoi Rimana”, Matem. sb., 71(113) (1966), 495–502 | MR | Zbl

[9] N. I. Muskhelishvili, Singulyarnye integralnye uravneniya, Nauka, Moskva, 1968 | MR | Zbl

[10] M. A. Shubin, “Faktorizatsiya zavisyaschikh ot parametra matrits-funktsii v normirovannykh koltsakh i svyazannye s nei voprosy teorii neterovskikh operatorov”, Matem.sb., 73(115) (1967), 610–629 | Zbl

[11] M. A. Shubin, “Ob indekse semeistv operatorov Vinera–Khopfa”, Matem. sb., 84(126) (1971), 537–558 | Zbl

[12] G. D. Birkhoff, “A theorem on matrices of analytic functions”, Math. Ann., 74 (1913), 122–133 | DOI | MR

[13] A. Grothendieck, “Sur la classification des fibres holomorphes sur la sphere de Riemann”, Amer. J. Math., 79:1 (1957), 121–138 | DOI | MR | Zbl

[14] H. Röhrl, “On holomorphic families of fiber bundles over the Riemannian sphere”, Mem. Coll. Sci. Univ. Kyoto, 33:3 (1961), 435–477 | MR | Zbl

[15] H. Röhrl, “Uber das Riemann–Privalovsche Randwertproblem”, Math. Ann., 151:5 (1963), 365–423 | DOI | MR

[16] G. N. Chebotarev, “Chastnye indeksy kraevoi zadachi Rimana s treugolnoi matritsei vtorogo poryadka”, Uspekhi .matem. nauk, XI:3(70) (1956), 190–202