On the index of families of Wiener–Hopf operators
Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 529-551 Cet article a éte moissonné depuis la source Math-Net.Ru

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A topological formula is obtained for the index of families of convolution operators on the halfline, enabling one to construct a homotopy invariant, depending on dimension, for multidimensional Wiener–Hopf equations on a halfspace and also to obtain examples of polynomial matrices with varying partial indices. Bibliography: 15 titles.
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M. A. Shubin. On the index of families of Wiener–Hopf operators. Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 529-551. http://geodesic.mathdoc.fr/item/SM_1971_13_4_a2/

[1] M. Atya, “Algebraicheskaya topologiya i ellipticheskie operatory”, Matematika, 12:5 (1968), 139–150

[2] M. Atya, Lektsii po $K$-teorii, Mir, Moskva, 1967 | MR

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

[4] L. S. Goldenshtein, “Priznaki odnostoronnei obratimosti funktsii ot neskolkikh izometricheskikh operatorov i ikh prilozheniya”, DAN SSSR, 155:1 (1964), 28–31 | Zbl

[5] L. S. Goldenshtein, “O mnogomernykh integralnykh uravneniyakh tipa Vinera–Khopfa”, Izv. AN Mold. SSR, 1964, no. 6, 27–38

[6] L. S. Goldenshtein, I. Ts. Gokhberg, “O mnogomernom integralnom uravnenii na poluprostranstve s yadrom, zavisyaschim ot raznosti argumentov, i ego diskretnom analoge”, DAN SSSR, 131:1 (1960), 9–12

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

[8] 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

[9] A. S. Dynin, “K teorii psevdodifferentsialnykh operatorov na mnogoobrazii s kraem”, DAN SSSR, 186:2 (1969), 251–253 | MR | Zbl

[10] N. Ya. Krupnik, “Sistemy mnogomernykh uravnenii tipa Vinera–Khopfa”, AN Mold. SSR, Matem. issledovaniya, II:4 (1967), 199–205 | MR

[11] S. P. Novikov, “Metody algebraicheskoi topologii s tochki zreniya teorii kobordizmov”, Izv. AN SSSR, seriya matem., 31 (1967), 855–951 | Zbl

[12] M. A. Shubin, “Ob indekse mnogomernykh uravnenii Vinera–Khopfa v poluprostranstve”, Uspekhi matem. nauk, XXIV:3(147) (1969), 222

[13] M. Atiyah, “Bott periodicity and the index of elliptic operators”, Quarterly J. Math., 19:74 (1968), 113–140 | DOI | MR | Zbl

[14] L. Illusie, “Complexes quasi-acycliques directs de fibres banachiques”, C. R. Acad. Sci., 260:1 (1965), 6499–6502 | MR | Zbl

[15] Shih Weishu, “Fiber cobordism and the index of a family of elliptic differential operators”, Bull. Amer. Math. Soc., 72 (1966), 984–991 | DOI | MR | Zbl