@article{ASNSP_1976_4_3_2_267_0, author = {Hartman, Philip}, title = {Completely monotone families of solutions of $n$-th order linear differential equations and infinitely divisible distributions}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {267--287}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 3}, number = {2}, year = {1976}, zbl = {0386.34016}, mrnumber = {404760}, language = {en}, url = {archive.numdam.org/item/ASNSP_1976_4_3_2_267_0/} }
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, Série 4, Tome 3 (1976) no. 2, pp. 267-287. http://archive.numdam.org/item/ASNSP_1976_4_3_2_267_0/
[1] A theorem on a differential inequality for multi-point boundary value problems, Izv. Vysš. Učebn. Zaved. Matematika, 2 (27) (1962), pp. 170-179 (Russian). | MR 143993
,[2] Disconjugacy, Lecture Notes in Mathematics, No. 220, Springer, 1971. | MR 460785 | Zbl 0224.34003
,[3] Stochastic Processes, Wiley, New York, 1953. | MR 58896 | Zbl 0053.26802
,[4] A. ERDELYI (editor), Higher Transcendental Functions, vol. 1, McGraw-Hill, New York, 1953. | Zbl 0051.30303
[5] Ordinary Differential Equations, Baltimore, 1973. | MR 344555 | Zbl 0281.34001
,[6] Unrestricted n-parameter families, Rend. Circ. Mat. Palermo (2), 7 (1958), pp. 123-142. | MR 105470 | Zbl 0085.04505
,[7] Principal solutions of disconjugate n-th order linear differential equations, Amer. J. Math., 91 (1969), pp. 306-362; 93 (1971), pp. 439-451. | MR 247181 | Zbl 0184.11603
,[8] On N-parameter families and interpolation problems for nonlinear ordinary differential equations, Trans. Amer. Math. Soc., 154 (1971), pp. 201-226. | MR 301277 | Zbl 0222.34017
,[9] « Normal » distribution functions on spheres and the modified Bessel functions, Ann. Prob., 2 (1974), pp. 593-607. | MR 370687 | Zbl 0305.60033
- ,[10] 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. | MR 146450 | Zbl 0125.32306
,[11] 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. | MR 254328 | Zbl 0195.37501
,[12] Elementary solutions for certain parabolic partial differential equations, Trans. Amer. Math. Soc., 82 (1950), pp. 519-548. | MR 87012 | Zbl 0070.32003
,[13] On a theorem of O. Arama, J. Differential Equations, 3 (1967), pp. 88-91. | MR 206375 | Zbl 0152.28103
,[14] Some estimates of the Green's functions o f a multipoint boundary value problem, Mat. Zametki, 4 (1968), pp. 533-540 (Russian). | MR 236453
[15] A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge, 1958. | Zbl 0174.36202
,[16] The Laplace Transform, Princeton, 1941. | MR 5923 | Zbl 0063.08245
,