×

zbMATH — the first resource for mathematics

Completely monotone families of solutions of \(n\)-th order linear differential equations and infinitely divisible distributions. (English) Zbl 0386.34016

MSC:
34A30 Linear ordinary differential equations and systems, general
46F10 Operations with distributions and generalized functions
PDF BibTeX XML Cite
Full Text: Numdam Numdam EuDML
References:
[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). MR 143993
[2] W.A. Coppel , Disconjugacy , Lecture Notes in Mathematics , No. 220 , Springer , 1971 . MR 460785 | Zbl 0224.34003 · Zbl 0224.34003
[3] J.L. Doob , Stochastic Processes , Wiley , New York , 1953 . MR 58896 | Zbl 0053.26802 · Zbl 0053.26802
[4] A. ERDELYI (editor), Higher Transcendental Functions , vol. 1 , McGraw-Hill , New York , 1953 . Zbl 0051.30303 · Zbl 0051.30303
[5] P. Hartman , Ordinary Differential Equations , Baltimore , 1973 . MR 344555 | Zbl 0281.34001 · Zbl 0281.34001
[6] P. Hartman , Unrestricted n-parameter families , Rend. Circ. Mat. Palermo ( 2 ), 7 ( 1958 ), pp. 123 - 142 . MR 105470 | Zbl 0085.04505 · Zbl 0085.04505 · doi:10.1007/BF02854523
[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 . MR 247181 | Zbl 0184.11603 · Zbl 0184.11603 · doi:10.2307/2373512
[8] P. Hartman , 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 · Zbl 0222.34017 · doi:10.2307/1995438
[9] P. Hartman - G.S. Watson , Normal distribution functions on spheres and the modified Bessel functions , Ann. Prob. , 2 ( 1974 ), pp. 593 - 607 . Article | MR 370687 | Zbl 0305.60033 · Zbl 0305.60033 · doi:10.1214/aop/1176996606 · minidml.mathdoc.fr
[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 . MR 146450 | Zbl 0125.32306 · Zbl 0125.32306
[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 . MR 254328 | Zbl 0195.37501 · Zbl 0195.37501 · doi:10.1070/RM1969v024n02ABEH001342
[12] H P. McKean Jr. , Elementary solutions for certain parabolic partial differential equations , Trans. Amer. Math. Soc. , 82 ( 1950 ), pp. 519 - 548 . MR 87012 | Zbl 0070.32003 · Zbl 0070.32003 · doi:10.2307/1993060
[13] Z. Opial , On a theorem of O. Arama , J. Differential Equations , 3 ( 1967 ), pp. 88 - 91 . MR 206375 | Zbl 0152.28103 · Zbl 0152.28103 · doi:10.1016/0022-0396(67)90008-3
[14] Ju V. Pokorny Some estimates of the Green’s functions o f a multipoint boundary value problem , Mat. Zametki , 4 ( 1968 ), pp. 533 - 540 (Russian). MR 236453 · Zbl 0176.05102 · doi:10.1007/BF01111315
[15] G.N. Watson , A Treatise on the Theory of Bessel Functions , 2 nd ed., Cambridge , 1958 . Zbl 0174.36202 · Zbl 0174.36202
[16] D. Widder , The Laplace Transform , Princeton , 1941 . MR 5923 | Zbl 0063.08245 · Zbl 0063.08245
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.