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

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1. [1] E.S. Či, A theorem on a differential inequality for multi-point boundary value problems, Izv. Vysš. Učebn. Zaved. Matematika, 2 (27) (1962), pp. 170-179 (Russian). MR143993
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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