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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

On the existence of a “wave operator” for the Boltzmann equation


Author: F. Alberto Grünbaum
Journal: Bull. Amer. Math. Soc. 78 (1972), 759-762
MSC (1970): Primary 45M05, 47H15, 82A40; Secondary 33A65, 60K35
MathSciNet review: 0309491
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  • 1. C. S. Wang Chang and G. E. Uhlenbeck, The kinetic theory of gases, Studies of Statistical Mechanics, vol. 5, North-Holland, Amsterdam, 1970.
  • 2. G. E. Uhlenbeck and G. W. Ford, Lectures in statistical mechanics, With an appendix on quantum statistics of interacting particles by E. W. Montroll. Lectures in Applied Mathematics (Proceedings of the Summer Seminar, Boulder, Colorado, vol. 1960, American Mathematical Society, Providence, R.I., 1963. MR 0151255 (27 #1241)
  • 3. F. Alberto Grünbaum, Linearization for the Boltzmann equation, Trans. Amer. Math. Soc. 165 (1972), 425–449. MR 0295718 (45 #4783), http://dx.doi.org/10.1090/S0002-9947-1972-0295718-5
  • 4. M. Kac, Foundations of kinetic theory, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. III, University of California Press, Berkeley and Los Angeles, 1956, pp. 171–197. MR 0084985 (18,960i)
  • 5. J. C. Maxwell, Scientific papers, Dover, New York. n. d.
  • 6. I. Talmi, Nuclear spectroscopy with harmonic oscillator wave functions, Helv. Phys. Acta 25 (1952), 185.
  • 7. Z. Alterman, K. Frankowski and C. L. Pekeris, Eigenvalues and eigenfunctions of the linearized Boltzmann collision operator, Astrophys. J. 7 (1962), Suppl. Ser. 291.
  • 8. K. Kumar, Ann. Physics 37 (1966), 113.
  • 9. F. Alberto Grünbaum, A property of Legendre polynomials, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 959–960. MR 0267164 (42 #2066)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1972-13021-0
PII: S 0002-9904(1972)13021-0