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Vector Moment Problems for Rapidly Decreasing Smooth Functions of Several Variables
Author(s):
Ricardo
Estrada
Journal:
Proc. Amer. Math. Soc.
126
(1998),
761-768.
MSC (1991):
Primary 30E05, 46F40
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Abstract:
The existence of rapidly decreasing smooth solutions of moment problems for functions of several variables with values in a Fréchet space is obtained. It is shown that the corresponding results for functions with values in a general topological vector space do not hold.
References:
- 1.
- N. I. Akhiezer, The Classical Moment Problem, Oliver and Boyd, Edinburgh, 1965.
- 2.
- A. J. Durán, The Stieltjes moments problem for rapidly decreasing functions, Proc. Amer. Math. Soc. 107 (1989), 731-741. MR 90b:44009
- 3.
- A. L. Durán and R. Estrada, Strong moment problems for rapidly decreasing smooth functions, Proc. Amer. Math. Soc. 120 (1994), 529-534. MR 94d:44005
- 4.
- R. Estrada, The asymptotic expansion of certain series considered by Ramanujan, Applicable Anal. 43 (1992), 191-228. MR 95i:46053
- 5.
- R. Estrada, J. M. Gracia-Bondía and J. C. Várilly, On asymptotic expansions of twisted products, J. Math. Phys. 30 (1989), 2789-2796. MR 91c:46057
- 6.
- R. Estrada and R. P. Kanwal, Moment sequences for a class of distributions, Complex Variables 9 (1987), 31-39. MR 89d:30041
- 7.
- R. Estrada and R. P. Kanwal, A distributional theory for asymptotic expansions, Proc. Roy. Soc. London A 428 (1990), 339-430. MR 91c:41085
- 8.
- R. Estrada and R. P. Kanwal, Asymptotic Analysis: a Distributional Approach, Birkhäuser, Boston, 1994. MR 95g:46071
- 9.
- A. Grothendieck, Produits Tensoriels Topologiques et Espaces Nucléaires, Memoirs of the Amer. Math. Soc. 16, Providence, RI, 1955. MR 17:763c
- 10.
- A. M. Krall, R. P. Kanwal and L. L. Littlejohn, Distributional solutions of ordinary differential equations, Can. Math. Soc. Conf. Proc. 8 (1987), 227-246. MR 89a:34040
- 11.
- L. L. Littlejohn and R. P. Kanwal, Distributional solutions of the hypergeometric differential equation, J. Math. Anal. Appl. 122 (1987), 325-345. MR 88b:33008
- 12.
- R. D. Morton and A. M. Krall, Distributional weight functions for orthogonals polynomials, SIAM J. Math. Anal. 9 (1978), 604-626. MR 58:12172
- 13.
- L. Schwartz, Théorie des Distributions, Hermann, Paris, 1957.
- 14.
- J. A. Shohat and J. D. Tamarkin, The Problem of Moments, Amer. Math. Soc., Providence, RI, 1943. MR 5:5c
- 15.
- F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967. MR 37:726
- 16.
- J. Wiener, Generalized function solutions of differential and functional differential equations, J. Math. Anal. Appl. 88 (1982), 170-182. MR 83g:34005
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Additional Information:
Ricardo
Estrada
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Address at time of publication:
P. O. Box 276, Tres Ríos, Costa Rica
Email:
restrada@cariari.ucr.ac.cr
DOI:
10.1090/S0002-9939-98-04109-4
PII:
S 0002-9939(98)04109-4
Received by editor(s):
May 25, 1995
Received by editor(s) in revised form:
September 3, 1996
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1998,
American Mathematical Society
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