van der Mee, Cornelis V. M. Transport theory in \(L_ p\)-spaces. (English) Zbl 0506.45011 Integral Equations Oper. Theory 6, 405-443 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 13 Documents MSC: 45J05 Integro-ordinary differential equations 82C70 Transport processes in time-dependent statistical mechanics 34G10 Linear differential equations in abstract spaces Keywords:time-independent neutron transport equation; operator differential equation; existence; uniqueness; subcritical media; vector-valued convolution equation; Fredholm operator Citations:Zbl 0363.45010 PDFBibTeX XMLCite \textit{C. V. M. van der Mee}, Integral Equations Oper. Theory 6, 405--443 (1983; Zbl 0506.45011) Full Text: DOI References: [1] H. Bart, I. Gohberg, M.A. Kaashoek: Minimal factorization of matrix and operator functions. Operator Theory: Advances and Applications 1, Birkhäuser Verlag, 1979. · Zbl 0424.47001 [2] J. Bognár: Indefinite inner product spaces. Heidelberg, Springer Verlag, 1974. [3] S. Chandrasekhar: Radiative transfer. Second revised edition. New York, Dover Publ., 1960. [4] J.J. Duderstadt, W.R. Martin: Transport theory. A Wiley -Interscience Publication, John Wiley & Sons, 1979. [5] N. Dunford, J.T. Schwarz: Linear operators. I. New York, Interscience, 1958. · Zbl 0084.10402 [6] I.A. Feldman: Wiener-Hopf operator equations and their application to the transport equation. Integral equations and operator theory 3, 43 - 61, 1980 = Matem. Issled. 6 (3), 115 –132, 1971 (Russian). · Zbl 0428.45009 [7] I.A. Feldman: On some projection methods for the solution of the equation of radiative energy transfer. Matem. Issled. 7 (4), 228 - 236, 1972 (Russian). [8] I.C. Gohberg, G. Heinig: On matrix integral equations on finite intervals with kernels depending on the difference of their arguments. Rev. Roum. Math. Pures et Appl. 20, 55 - 73, 1975 (Russian). [9] I.C. Gohberg, M.G. Krein: Systems of integral equations on a half-line with kernels depending of the difference of arguments. A.M.S. Transl. 14, 217 -287, 1960 = Uspehi Matem. Nauk 13 (2), 3 – 72, 1959 (Russian). [10] I.C. Gohberg, J. Leiterer: Factorization of operator functions with respect to a contour. II. Canonical factorization of operator functions, close to the identity. Math. Nachrichten 54, 41 - 74, 1972 (Russian). · Zbl 0243.47015 [11] I.C. Gohberg, J. Leiterer: Factorization of operator functions with respect to a contour. III. Factorization in algebras. Math. Nachrichten 55, 33 - 61, 1973 (Russian). · Zbl 0251.47013 [12] I.C. Gohberg, E.I. Sigal: An operator generalization of the logarithmic residue theorem and the theorem of Rouché. Math. USSR Sbornik 13, 603 - 625, 1971 = Mat. Sbornik 84 (126), 607 - 629, 1971 (Russian). · Zbl 0254.47046 [13] W. Greenberg, P.F. Zweifel: Functional-analytic treatment of the transport equation. Transport Theory and Statistical Physics 5, 219 - 253, 1976. · Zbl 0348.45018 [14] R.J. Hangelbroek: Linear analysis and solution of neutron transport problems. Transport Theory and Statistical Physics 5, 1 - 85, 1976. · Zbl 0363.45010 [15] R.J. Hangelbroek: On the derivation of some formulas in linear transport theory for media with anisotropic scattering. Report 7720, University of Nijmegen, The Netherlands, 1978. · Zbl 0427.34024 [16] H.C. van de Hulst: Multiple light scattering: tables, formulas and applications. I, II. New York, Academic Press, 1980. [17] T. Kato: Perturbation theory for linear operators. Heidelberg, Springer Verlag, 1966. · Zbl 0148.12601 [18] E.W. Larsen: Solutions of neutron transport problems inL 1. Comm. on Pure and Appl. Math. 28, 729 - 746, 1975. · Zbl 0345.45011 [19] E.W. Larsen: S. Sancaktar, P.F. Zweifel: Extension of the Case formulas toL p. Application to half- and full-space problems. J. Math. Phys. 16, 1117 - 1121, 1975. · Zbl 0311.47025 [20] C.G. Lekkerkerker: The linear transport equation. The degenerate case c = 1. I. Full-range theory; II. Half-range theory. Proc. Royal Soc. Edinburgh 75 A, 259 - 282 & 283 – 295, 1975. · Zbl 0335.47033 [21] M.V. Maslennikov: The Milne problem with anisotropic scattering. Proc. of the Steklov institute of mathematics, vol. 97, 1968 = Trudy matem. instituta im. V.A. Steklova, AN SSSR, 97, 1968 (Russian). · Zbl 0187.07901 [22] C.V.M. van der Mee: Semigroup and factorization methods in Transport Theory. Amsterdam, Mathematical Centre Tract 146, 1981. · Zbl 0481.45008 [23] V.V. Sobolev: Light scattering in planetary atmospheres. Oxford, Pergamon Press, 1975. [24] K. Stummel: Discrete convergence of linear operators, II. Math. Zeitschrift 120, 231 - 264, 1971 (German). · Zbl 0209.15502 [25] A.E. Taylor: Introduction to functional analysis. New York, John Wiley & Sons, 1964. [26] V.S. Vladimirov: Mathematical problems of the one-speed particle transprt theory. Trudy matem. instituta im. V.A. Steklova, AN SSSR, 61, 1961 (Russian). [27] A.C. Zaanen: Integration. Amsterdam, North-Holland, 1967. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.