Advertisement

My mathematical expectations

  • H. L. Turrittin
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 312)

Keywords

Ordinary Linear Differential Equation Regular Singularity Linear Differential System Irregular Singular Point Formal Series Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H.L. Turrittin. "Asymptotic solutions of certain ordinary differential equations associated with multiple roots of the characteristic equations," Amer. Jour. of Math., 58 (1936) 364–376.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    _____, "Asymptotic distribution of zeros for certain exponential sums," Amer. Jour. of Math., 66 (1944) 199–228.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    H.L. Turrittin. "Stokes multipliers for asymptotic solutions of a certain differential equation," Trans, Amer. Math. Soc., 68 (1950) 304–329.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    _____ "Asymptotic expansions of solutions of ordinary linear differential equations containing a parameter," Annals of Math. Studies, vol. II, No. 29, Princeton: Princeton Univ. Press, (1952) 81–116.Google Scholar
  5. 5.
    _____ "Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point," Acta Mathematica, 93 (1955) 27–66.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    _____ "A peculiar solution of a modified Duffing's equation" (with W.J.A. Culmer), Ann Mat. Pura Appl. Ser. IV, 44 (1957) 23–33.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    _____ "Standardization and simplification of systems of linear differential equations involving a turning point" (with W.A. Harris, Jr.), SIAM J. Appl. Math 7 (1959) 316–324.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    _____ "Linear differential or difference equations with constant coefficients," Amer. Math. Monthly, 66 (1959) 869–875.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    _____ "The formal theory of systems of irregular homogeneous linear difference and differential equations," Boletin de la Sociedad Math. Mexicana, (1960) 255–264.Google Scholar
  10. 10.
    _____ "A canonical form for a system of linear difference equations," Ann. Mat. Pura Appl. Ser. IV, 58 (1962) 335–358.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    _____ "Reduction of ordinary differential equations to the Birkhoff canonical form," Trans. Amer. Math. Soc., 107 (1963) 485–507.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    _____ "Solvable related equations pertaining to turning point problems," Asymptotic solutions of differential equations and their applications, edited by Calvin H. Wilcox, John Wiley & Sons, (1964) 27–52.Google Scholar
  13. 13.
    H.L. Turrittin. "Stokes multipliers for the differential equation dny / dxn − y/x=0," Funkcialaj Ekvacioj, 6 (1964) 37–46.MathSciNetGoogle Scholar
  14. 14.
    _____ "Convergent solutions of ordinary linear nonhomogeneous differential equations," Funkcialaj Ekvacioj, 12 (1969) 7–21.MathSciNetzbMATHGoogle Scholar
  15. 15.
    R.E. Langer. "The solution of the differential equation v‴+λzv′+3μλ2v=0 " Duke Math. J. 22 (1955) 525–542.MathSciNetCrossRefGoogle Scholar
  16. 16.
    _____ "On the asymptotic forms of ordinary linear differential equations of the third order in a region containing a turning point," Trans. Amer. Math. Math. Soc., 80 (1955) 93–123.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    _____ "The solutions of a class of ordinary linear differential equations of the third order in a region containing a multiple turning point," Duke Math. J. 23 (1956) 93–110.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    _____ "On the asymptotic solutions of a class of ordinary differential equations of the fourth order with a special reference to an equation of hydrodynamics," Trans. Amer. Math. Soc. 84 (1957) 144–191.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Y. Sibuya. "Simplification of a linear ordinary differential equation of the n-th order at a turning point," Arch. Rat. Mech. Anal., 13 (1963) 206–221.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    _____ "On the problem of turning points for a system of linear ordinary differential equations of higher orders," Proc. of Symposium Math. Res. Ctr., U.S. Army, Univ. Wisconsin, Madison, Wisc. (1964) 145–162, Wiley, N.Y. 1964.Google Scholar
  21. 21.
    W. Wasow. Asymptotic expansions for ordinary differential equations, Interscience Publishers, 1965, Chap. 8.Google Scholar
  22. 22.
    _____ "On turning point problems for systems with almost diagonal coefficient matrix," Funkcialaj Ekvacioj, 8 (1966) 143–170.MathSciNetzbMATHGoogle Scholar
  23. 23.
    _____ "The central connection problem at turning points of linear differential equations," Analytic theory of differential equation, Lecture notes in Mathematics, #183, Springer-Verlag, 1971, (Proc. of a conference at Western Mich. Univ.), 158–164.Google Scholar
  24. 24.
    L.A. MacColl. "On the distribution of the zeros of sums of exponentials of polynomials," Trans. Amer. Math. Soc., 36 (1934) 341–360.MathSciNetzbMATHGoogle Scholar
  25. 25.
    R.E. Langer. "The asymptotic location of the roots of a certain transcendental equation," Trans. Amer. Math. Soc., 31 (1929) 837–844.MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    J.G. Van der Corput. "Rhythmische Systeme," Acta Math. 59 (1932) 209–328.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    J.B. McLeod. "On the distribution of eigenvalues of an n-th order equation," Quart, J. Math. Oxford (2), 17 (1966) 112–131.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    B.L.J. Braaksma. "Asymptotic analysis of a differential equation of Turrittin," SIAM J. Math. Anal, 2 (1971) 1–16.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    H.L. Turrittin. "Stokes multipliers for the equation d3y/dx3 − y/x2=0," Lecture notes in mathematics, #183, Analytic theory of differential equations, (Proc. of Conf. at Western Mich. Univ. (1970) 145–157.Google Scholar
  30. 30.
    H. Scheffé. "Linear differential equations with two term recurrence formulas," J. Math. & Phys., 21 (1942) 240–249.MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    W. Loud & K.W. Blair. "Periodic solutions of x″ + cx′ + g(x)=Ef(t) under variation of certain parameters," SIAM J. Appl. Math. 8 (1960) 74–101.MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    W. Loud. "Periodic solutions of second order differential equations of Duffing type," Proc. U.S.-Japan Seminar, (1967) 199–224.Google Scholar
  33. 33.
    _____ "Branching phenomena for periodic solutions of nonautonomous piecewise linear systems," International Jour. of Nonlinear Mechanics, 5 (1969) 352–368.MathSciNetzbMATHGoogle Scholar
  34. 34.
    W.J.A. Culmer & W.A. Harris, Jr. "Convergent solutions of ordinary linear homogeneous difference equations," Pac. Jour. Math., 13 (1963) 1111–1138.MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    W.A. Harris, Jr. & S. Tanaka. "On difference equations containing a parameter," Publ. of Research Inst. for Math. Sciences, Kyoto Univ., Ser. A, 2 (1966), 5–16.MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    R. Gérard & A.H.M. Levelt. "Invariants mesurant l'irregularité en un point singulier des systemes d'équations différentielles linéariares," Notes published by the Institut de Recherche Mathématique Avancée de Strasbourg, 1972.Google Scholar
  37. 37.
    A.H.M. Levelt. "Formal theory of irregular singular points," (to appear), 1972.Google Scholar
  38. 38.
    H.L. Turrittin. "Reducing the rank of ordinary differential equations," Duke Math. Jour., 30 (1963) 271–274.MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    D.A. Lutz. "On the reduction of rank of linear differential systems," U.S. Army Math. Research Center, Univ. of Wisc., Madison, Wisc., Report #1097, Aug., 1970, 1–18.Google Scholar
  40. 40.
    G.D. Birkhoff, "Equivalent singular points of ordinary linear differential equations," Math. Ann. 74 (1913), p. 136.MathSciNetGoogle Scholar
  41. 41.
    W.B. Jurkat & D.A. Lutz. "Birkhoff reduction of two-dimensional linear differential systems at a singular point," U.S. Army Math. Research Center, Univ. of Wisc., Madison, Wisc., Report #1062, (1970), 1–33.Google Scholar
  42. 42.
    E.L. Ince. Ordinary Differential Equations, 1927 edition, p. 174.Google Scholar
  43. 43.
    K.O. Friedrichs. Special topics in analysis, New York Univ. Notes, 1953, page B-9.Google Scholar
  44. 44.
    L.M. Milne-Thompson. The calculus of finite differences, 1951, pp. 289–290.Google Scholar
  45. 45.
    W.A. Harris, Jr., Y. Sibuya & L Weinberg. "Holomorphic solutions of Linear differential systems at singular points," Arch. Rat. Mech. & Anal, 35 (1969), 245–248.MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    F. Lettenmeyer. "Über die an einer Unbestimmtheitsstelle regulären Lösungen eines Systemes homogener linearen Differentialgleichunghen," S.-B. Bayer. Akad. Wiss. Munchen Math.-nat. Abt. (1926) 287–307.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • H. L. Turrittin

There are no affiliations available

Personalised recommendations