Oscillator Basis in the J-Matrix Method: Convergence of Expansions, Asymptotics of Expansion Coefficients and Boundary Conditions

  • S.Yu. Igashov


Important mathematical aspects of the J-matrix method are considered in the case of the oscillator basis. The asymptotic form of the Fourier coefficients for the expansions over the oscillator basis is found by the use of the asymptotic approximations for the basis functions. These results are applied to investigation of the pointwise convergence of the expansions.


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  1. 1.
    H.A. Jamani and L. Fishman, J. Math. Phys., 16, 410 (1975).CrossRefADSGoogle Scholar
  2. 2.
    V.S. Vasilevsky, G.F. Filippov, and L.L. Chopovsky, Sov. J. Part.Nucl., 16, 153 (1985); ibid., 15, 1338 (1984).Google Scholar
  3. 3.
    I.P. Okhrimenko, Nucl. Phys. A, 424, 121 (1984).CrossRefADSGoogle Scholar
  4. 4.
    S.Yu. Igashov and Yu.M. Tchuvil’sky, Bull. Russ. Acad. Sci.,Phys., 66(3), 385 (2002).Google Scholar
  5. 5.
    S.Yu. Igashov and A.M. Shirokov, Bull. Russ. Acad. Sci., Phys.,71(6), 797 (2007).CrossRefGoogle Scholar
  6. 6.
    Y.A. Lurie and A.M. Shirokov, Ann. Phys., 312(2), 284 (2004).MATHCrossRefADSGoogle Scholar
  7. 7.
    V.S. Vasilevsky and F. Arickx, Phys. Rev. A, 55(1),265(1997).CrossRefADSGoogle Scholar
  8. 8.
    J. Broeckhove, F. Arickx, W. Vanroose and V.S. Vasilevsky, J. Phys. A,37(31), 7769 (2004).MATHCrossRefADSMathSciNetGoogle Scholar
  9. 9.
    S.A. Zaytsev, Theor. Math. Phys., 140(1), 918 (2004).CrossRefGoogle Scholar
  10. 10.
    A.M. Shirokov, A.I. Mazur, S.A. Zaytsev, J.P. Vary, and T.A. Weber,Phys. Rev. C, 70(4), 044005 (2004).CrossRefADSGoogle Scholar
  11. 11.
    S.A. Zaytsev, Inverse Probl., 21(3), 1061 (2005).MATHCrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Shirokov, J.P. Vary, A.I. Mazur, S.A. Zaytsev, and T.A. Weber, J. Phys. G, 31(8), 1283 (2005).Google Scholar
  13. 13.
    N. Barnea, W. Leidemann, and G. Orlandini, Phys. Rev. C,74(3), 034003 (2006).Google Scholar
  14. 14.
    A. Erdelyi, Ed., Higher Transcendental Functions, Vol. II (Mc Graw-Hill, New York, 1953).Google Scholar
  15. 15.
    M. Abramowitz and I.A. Stegun, Eds., Handbook of Mathematical Functions, (Dover, New York, 1965).Google Scholar
  16. 16.
    G. Szego, Orthogonal Polynomials, Am. Math. Soc. Colloq. Publ.,Vol. 23, 4th ed. (AMS, Providence, RI, 1975).Google Scholar
  17. 17.
    F.W.J. Olver, Asymptotics and Special Functions (Academic, London,1974).Google Scholar
  18. 18.
    S.Yu. Igashov, Int. Transf. Spec. Funct., 8, 209(1999).MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    A. Erdelyi, J. Indian Math. Soc., 24, 235 (1960).Google Scholar
  20. 20.
    A.P. Prudnikov, Yu.A. Brychkov, and O.I. Marichev, Integrals and Series, Vol. 2 (Gordon and Breach, New York, 1986).Google Scholar
  21. 21.
    A.P. Prudnikov, Yu.A. Brychkov, and O.I. Marichev, Integrals and Series, Vol. 1 (Gordon and Breach, New York, 1986).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • S.Yu. Igashov
    • 1
  1. 1.Moscow Engineering Physics InstituteMoscow 115409Russia

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