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An Extension Problem For Functions With Monotonic Derivatives

Published online by Cambridge University Press:  20 November 2018

W. B. Jurkat
W. B. Jurkat*
Affiliation:
University of Cincinnati
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Introduction. This paper deals with questions of the following type. Problem (A) : Let F(x) be the nth integral of a positive non-decreasing function for all large positive x, the problem is to find a function f(x), being the nth integral of a non-decreasing function for all x (— ∞ < x < ∞), with the property

A.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 184 - 191
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Achyeser, N. and Krein., M. Über eine Transformation der reellen Toeplitzschen Formen und das Momentenproblem in einem endlichen Intervalle, Commun. Soc. Math. Kharkoff (4), 11 (1935), 21–26.Google Scholar
2. Hardy, G. H., Orders of infinity (Cambridge Tract, 1924).Google Scholar
3. Kantorovič, L., On the moment problem for a finite interval, C. R. (Doklady), Acad. Sci. URSS (N.S.), 14 (1937), 531–537.Google Scholar
4. Kowalewski, G., Integralgleichungen (Berlin, ).Google Scholar
5. Krein, M., The ideas of P. L. Čebyšev and A. A. Markov in the theory of limiting values of integrals and their further development, Upsekhi Matem. Nauk (N.S.) 6 (1951), 3–120.Google Scholar
6. Shohat, J. A. and Tamarkin, J. D., The problems of moments (New York, 1943).Google Scholar
7. Verblunsky, S., On a problem of moments, Proc. Cambridge Philos. Soc. 45 (1949), 1–4.Google Scholar
8. Widder, D. V., The Laplace transform (Princeton, 1946).Google Scholar