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Original Articles

Albedo operators and H-equations for generalized kinetic models

Pages 341-376 | Received 19 Oct 1983, Published online: 06 Dec 2011

References

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  • van der Mee , C. V. M. 1980 . Int. Eqs. Oper. Theor. , 3 : 529
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  • Condition (1.17) implies ∥H(t)B∥ dt<∞, see also the Appendix
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  • Gohberg , I. C. and Leiterer , J. 1973 . Math. Nachrichten , 55 : 33 A(z) has, indeed, a Wiener-Hopf factorization, The convolution kernel H(t)B is compact and Bochner integrable on (-∞,∞) (see Lemma A. 2), while A(z) is invertible for izϵ[-∞,∞]. According to Theorem 4.3 (or 4.4) of
  • Gohberg , I. C. and Leiterer , J. 1972 . Math. Nachrichten , 54 : 41 Theorem 4.1
  • Ibid., Appendix, where a new proof appears of a result of Allan, Bochner and Phillips. See Ref. 29 for the references to the latter work
  • Note the following:[(I-L+)f](x) = e-xT −1Q+h(x>0) for some hϵD(T), if and only if f(0)ϵRan X+xD(T) and Q+f(0) = Q+h. So Q+h = f(0)-Q−f(0) belongs to [X++Ran Q] xD(T). Further, if (l-L+)f=0, then f(x)ϵD(T), and thus both f(Ō)ϵX+n D(T) and Q+f(0) = 0. So f (0)EX+x Ran Q− ⊆ D(T)
  • van der Mee , C. V. M. 1983 . Int. Eqs. Oper. Theor. , 6 : 405
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  • A reduction of this kind appeared before in Refs. 3,4 and 33
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  • Greenberg , W. and van der Mee , C. V. M. “An Abstract Approach to Evaporation Models in Rarefied Gas Dynamics” . Zeitschr. Angew. Math. Phys. , Vol. 35 to appear in
  • Diestel , J. and Uhl , J. J. 1977 . “Vector Measures” , Providence , R.I. : A.M.S. . Lemma 6

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