Completely monotone families of solutions of n -th order linear differential equations and infinitely divisible distributions

Philip Hartman

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1976)

  • Volume: 3, Issue: 2, page 267-287
  • ISSN: 0391-173X

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Hartman, Philip. "Completely monotone families of solutions of $n$-th order linear differential equations and infinitely divisible distributions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.2 (1976): 267-287. <http://eudml.org/doc/83719>.

@article{Hartman1976,
author = {Hartman, Philip},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {2},
pages = {267-287},
publisher = {Scuola normale superiore},
title = {Completely monotone families of solutions of $n$-th order linear differential equations and infinitely divisible distributions},
url = {http://eudml.org/doc/83719},
volume = {3},
year = {1976},
}

TY - JOUR
AU - Hartman, Philip
TI - Completely monotone families of solutions of $n$-th order linear differential equations and infinitely divisible distributions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1976
PB - Scuola normale superiore
VL - 3
IS - 2
SP - 267
EP - 287
LA - eng
UR - http://eudml.org/doc/83719
ER -

References

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  2. [2] W.A. Coppel, Disconjugacy, Lecture Notes in Mathematics, No. 220, Springer, 1971. Zbl0224.34003MR460785
  3. [3] J.L. Doob, Stochastic Processes, Wiley, New York, 1953. Zbl0053.26802MR58896
  4. [4] A. ERDELYI (editor), Higher Transcendental Functions, vol. 1, McGraw-Hill, New York, 1953. Zbl0051.30303
  5. [5] P. Hartman, Ordinary Differential Equations, Baltimore, 1973. Zbl0281.34001MR344555
  6. [6] P. Hartman, Unrestricted n-parameter families, Rend. Circ. Mat. Palermo (2), 7 (1958), pp. 123-142. Zbl0085.04505MR105470
  7. [7] P. Hartman, Principal solutions of disconjugate n-th order linear differential equations, Amer. J. Math., 91 (1969), pp. 306-362; 93 (1971), pp. 439-451. Zbl0184.11603MR247181
  8. [8] P. Hartman, On N-parameter families and interpolation problems for nonlinear ordinary differential equations, Trans. Amer. Math. Soc., 154 (1971), pp. 201-226. Zbl0222.34017MR301277
  9. [9] P. Hartman - G.S. Watson, « Normal » distribution functions on spheres and the modified Bessel functions, Ann. Prob., 2 (1974), pp. 593-607. Zbl0305.60033MR370687
  10. [10] A. Yu. Levin, Some problems bearing on the oscillation of solutions of linear differential equations, Dokl. Akad. Nauk SSSR, 148 (1963), pp. 512-515; Soviet Math. Dokl., 4 (1963), pp. 121-124. Zbl0125.32306MR146450
  11. [11] A. Yu. Levin, Nonoscillation of solutions of the equation x(n) +p1(t)x(n-1)+...= 0, Uspechi Mat. Nauk, 24 (1969), No. 2 (1946), pp. 43-96; Russian Math. Surveys, 24 (1969), pp. 43-99. Zbl0195.37501MR254328
  12. [12] H P. McKean Jr., Elementary solutions for certain parabolic partial differential equations, Trans. Amer. Math. Soc., 82 (1950), pp. 519-548. Zbl0070.32003MR87012
  13. [13] Z. Opial, On a theorem of O. Arama, J. Differential Equations, 3 (1967), pp. 88-91. Zbl0152.28103MR206375
  14. [14] Ju V. PokornySome estimates of the Green's functions o f a multipoint boundary value problem, Mat. Zametki, 4 (1968), pp. 533-540 (Russian). MR236453
  15. [15] G.N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge, 1958. Zbl0174.36202
  16. [16] D. Widder, The Laplace Transform, Princeton, 1941. Zbl0063.08245MR5923

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