Asymptotic expansion of fundamental solutions of higher order heat equations

Random Operators and Stochastic Equations

Volumn 5, Issue 3, 1997, Pages 217-226

  Accetta, Gabriele ^a   Orsingher, Enzo ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001922660     PISSN: 09266364     EISSN: 1569397X     Source Type: Journal    
DOI: 10.1515/rose.1997.5.3.217     Document Type: Article

References (18)

1. J. Bernstein. Über das Fourier integral costeda;, Math. Ann. 79, 265-268 (1919).
2. N. Bleistein and R. A. Handelsman. Asymptotic expansion of integrals. Dover, New York (1986).
3. W. R. Burwell. Asymptotic expansions of generalized hypergeometric functions, Proc. Lond. Math. Soc. 22, 57-72 (1923).
4. Yu. L. Daletskii. Functional integrals connected with operator evolution equations, Russian Mathematical Surveys, 1-107 (1962).
5. Yu. L. Daletskii and S. V. Fomin. Generalized measures in function spaces, Theory of Probability and its Applications, 10, 304-316 (1965).
6. Yu. L. Daletskii. Integration in function spaces, Progress in mathematics, vol. 4, 86-132 (1969). (Ed. R. V. Gamkrelidze.)
7. C. W. Gardiner. Handbook of stochastic methods for physics, chemistry and the natural sciences. Springer Verlag, Berlin (1985).
8. K. J. Hochberg. A signed measure on path space related to Wiener measure, The Annals of Probability 6, 433-458 (1978).
9. K. J. Hochberg, E. Orsingher. The arc-sine law and its analogs for processes governed by signed and complex measures, Stochastic Process and their Applications 52, 273-292 (1994).
10. V. Yu. Krylov. Some properties of the distribution corresponding to the equation |= (-i)+i 1 Dokl. Akad. Nauk SSSR 132, 6, 760-763 (1960). (In Russian).
11. V. Yu. Krylov. Integration of analytic functionals on sign-alternating distributions, Dokl. Akad. Nauk SSSR, 163, 2, 289-292 (1965). (In Russian).
12. V. I. Ladokhin. On nonpositive distributions, Uch. Zap. Kazan. Univ. 122, 4, 53-64 (1962). (In Russian).
13. V. I. Ladokhin. Generalization of some theorems of probability theory in the case of complex distributions, Uch. Zap. Kazan. Univ. 125, 6, 94-100(1965). (In Russian).
14. P. Levy. Sur une application de la derivee d'ordre non entier au calcul des probabilites, C.R. Acad. Sei. 176, 1118-1120 (1923).
15. X. Li, R. Wong. Asymptotic behaviour of the fundamental solution to |-(-A)mu, Proc. Roy. Soc. London A, 441, 423-432 (1993).
16. M. Miyamoto. An extension of cetain quasi-measure, Proceedings of the Japan Academy 42, 70-74 (1966).
17. E. Orsingher. Processes governed by signed measures connected with third-order "heat-type" equations, Lithuanian mathematical Journal 31, 220-231 (1991).
18. G. Pölya. On zeros of an integral function represented by Fourier's integral, Messenger Math., 52, 185-188 (1923).