References
Chandrasekhar, S.: Radiative transfer, Oxford, 1950.
Maslennikov, M.V.: The Milne problem with anisotropicscattering. Proc. Steklov Inst. Math. 97 (1968) English translation, Providence: Amer. Math. Soc., 1969.
Krein, M.G.: Integral equations on a half-line with kernel depending upon the difference of the arguments, Uspehi Mat. Nauk 13 (1958), no.5 (83), 3–120; English translation, Amer. Math. Soc. Transl. (2) 22 (1962), 163–288. MR 21 # 1507.
Gohberg, I.C., Krein, M.G.: Systems of integral equations on a half line with kernels depending on the difference of arguments, Uspehi Mat. Nauk 13 (1958), no.2 (80), 3–72; English Translation., Amer. Math. Soc. Transl. (2) 14 (1960), 217–287. MR 21 # 1506; 22 # 3954.
Fel'dman, I.A.: The asymptotics of solutions of systems of integral equations of Wiener-Hopf type, Sibirsk. Mat. Z. 6 (1965), 596–615. (Russian) MR 31 # 3808.
Vladimirov, V.S.: Mathematical problems of the uniformspeed theory of particle transport. Trudy Matem. Instituta im. V.A. Steklova AN SSSR, No. 61, 1961. (Russian)
Kantorovic, L.V. and Akilov, G.P.: Functional analysis in normed spaces. English translation, Internat. Series of Monographs in Pure and Appl. Math., vol. 46, Macmillan, New York, 1964. MR 22 # 9837; 35 # 4699.
Hille, E. and Phillips, R.S.: Functional analysis and semigroups, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, R.I., 1957.
Gohberg, I.C.: The problem of factorization of operator functions. Izvestia AN SSR, Serija matem., 28, No.5, 1964, 10055–1082 (Russian).
Budjanu, M.S.: Solution of certain classes of Wiener-Hopf equations with operator coefficients. Izvestia AN MSSR, 1966, No.4, 18–31. (Russian)
Keldys, M.V.: On the characteristic values and characteristic functions of certain classes of non-self-adjoint equations, Dokl. Akad. Nauk SSSR 77 (1951), 11–14, MR 12, 835 (Russian)
Eni, V.M.: On the stability of the root number of an analytical operator function and on perturbations of their characteristic numbers and eigenvectors. Dokl. Akad. Nauk SSSR, 173. No. 6, 1967, 1251–1254. (Russian)
Gohberg, I.C., and Krein, M.G.: Introduction to the theory of nonselfadjoint operators in a Hilbert space. English translation, Transl. Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R.I., 1969. MR 36 # 3137.
Markus, A.S.: On holomorphic operator functions, Dokl. Akad. Nauk SSSR 119 (1958), 1099–1102. MR 21 # 3772 (Russian).
Trofimov, V.P.: On root subspaces of operators, analytically depending on parameters. Kishinev, Matem. Issled. No.3, 1968, 117–125. (Russian)
Gahov, F.D. and Cerskii, Yu. I.: Singular integral equations of the convolution type. Izvestia AN SSSR, Serija matem., 20, No. 1, 1956, 33–52. (Russian)
Bochner, S. and Phillips, R.S.: Absolutely convergent Fourier expansions for non-commutative normed rings. Ann. of Math., 43, No.3, 1942, 409–418.
Savchenko, Yu. B.: A homogeneous semi-boundary problem for equations in a Banach space. Trudy seminara po funkc. analizu. Voronez, No. 10, 1968, 146–159. (Russian)
Fel'dman, I.A.: An equation of radiation energy transfer and Wiener-Hopf operator equations. Funkcional. Anal. i Prilozen. 5 (1971), no.3, 106–108 = Functional Anal. Appl. 5 (1971), 262–264. MR 44 # 858.
Additional information
Note of the editor: This paper was originally published in Russian in Mat. Issled, Kishinev, vol. 6, No.3, 1971, pp. 115–132. The editor is grateful to G. Lekkerker, L. Lerer and R. Troelstra for their work in translating this paper.
Rights and permissions
About this article
Cite this article
Feldman, I.A. Wiener-Hopf operator equations and their application to the transport equation. Integr equ oper theory 3, 43–61 (1980). https://doi.org/10.1007/BF01682871
Issue Date:
DOI: https://doi.org/10.1007/BF01682871