Geodesic
Generalization of the Hausdorff Moment Problem
Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 946-960

Voir la notice de l'article provenant de la source Cambridge University Press

Suppose throughout that {kn } is a sequence of positive integers, that that k 0 = 1 if l 0 = 1, and that {un (r)}; (r = 0, 1, ..., kn – 1, n = 0, 1, ...) is a sequence of real numbers. We shall be concerned with the problem of establishing necessary and sufficient conditions for there to be a function a satisfying (1) and certain additional conditions. The case l 0 = 0, kn = 1 for n = 0, 1, ... of the problem is the version of the classical moment problem considered originally by Hausdorff [5], [6], [7]; the above formulation will emerge as a natural generalization thereof. 
Borwein, David; Jakimovski, Amnon. Generalization of the Hausdorff Moment Problem. Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 946-960. doi: 10.4153/CJM-1981-075-0
@article{10_4153_CJM_1981_075_0,
     author = {Borwein, David and Jakimovski, Amnon},
     title = {Generalization of the {Hausdorff} {Moment} {Problem}},
     journal = {Canadian journal of mathematics},
     pages = {946--960},
     year = {1981},
     volume = {33},
     number = {4},
     doi = {10.4153/CJM-1981-075-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-075-0/}
}
TY  - JOUR
AU  - Borwein, David
AU  - Jakimovski, Amnon
TI  - Generalization of the Hausdorff Moment Problem
JO  - Canadian journal of mathematics
PY  - 1981
SP  - 946
EP  - 960
VL  - 33
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-075-0/
DO  - 10.4153/CJM-1981-075-0
ID  - 10_4153_CJM_1981_075_0
ER  - 
%0 Journal Article
%A Borwein, David
%A Jakimovski, Amnon
%T Generalization of the Hausdorff Moment Problem
%J Canadian journal of mathematics
%D 1981
%P 946-960
%V 33
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-075-0/
%R 10.4153/CJM-1981-075-0
%F 10_4153_CJM_1981_075_0

[1] 1. Berman, D. L., Application of interpolatory polynomial operators to solve the moment problem, Urkain Math. Z. 14 (1963), 184–190. Google Scholar

[2] 2. Borwein, D., The Hausdorff moment problem, Can. Math. Bull. 21 (1978), 257–265; Corrections 22 (1979), 128. Google Scholar

[3] 3. Davis, P. J., Interpolation and approximation (Blaisdell, New York, 1965). Google Scholar

[4] 4. Endl, K., On systems of linear inequalities in infinitely many variables and generalized Hausdorff means, Math. Z. 82 (1963), 1–7. Google Scholar

[5] 5. Hausdorff, F., Summationsmethoden und Moment﹜olgen I, Math. Z. 9 (1921), 74–109. Google Scholar

[6] 6. Hausdorff, F., Summationsmethoden und Momentfolgen II, Math. Z. 9 (1921), 280–299. Google Scholar

[7] 7. Hausdorff, F., Momentprobleme fur ein eindliches Interval, Math. Z. 16 (1923), 220–248. Google Scholar

[8] 8. Krasnosel'skii, M. A. and Rutickk, Ya. B., Convex functions and Orlicz spaces (P. Noordhoff, Groningen, 1961). Google Scholar

[9] 9. Leviatan, D., A generalized moment problem, Israel J. Math. 5 (1967), 97–103. Google Scholar

[10] 10. Leviatan, D., Some moment problems in a finite interval, Can. J. Math. 20 (1968), 960–966. Google Scholar

[11] 11. Lorentz, G. G., Bernstein polynomials (University of Toronto Press, Toronto, 1953). Google Scholar

[12] 12. Medvedev, U. T., Generalization of a theorem of F. Riesz, Uspeshi, Mat. Nauk 8 (1953), 115–118. Google Scholar

[13] 13. Schoenberg, I. J., On finite rowed systems of linear inequalities in infinitely many variables, Trans. A.M.S. 34 (1932), 594–619. Google Scholar

[14] 14. Widder, D. V., The Laplace transform (Princeton, 1946). Google Scholar

[15] 15. Zygmund, A., Trigonometric series I, 2nd edition (Cambridge University Press, Cambridge, 1959). Google Scholar

Cité par Sources :