Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the expansion of functions in terms of their moments

Author: H. S. Green
Journal: Quart. Appl. Math. 11 (1954), 403-409
MSC: Primary 41.1X
DOI: https://doi.org/10.1090/qam/58025
MathSciNet review: 58025
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Abstract: A general method is devised for the reconstruction of functions of a continuous variable from their moments. An analogue is given for functions of a discrete variable. An application is given to the solution of partial differential equations with a given initial condition.

References [Enhancements On Off] (What's this?)

  • [1] J. A. Shohat and J. D. Tamarkin, The Problem of Moments, American Mathematical Society Mathematical surveys, vol. I, American Mathematical Society, New York, 1943. MR 0008438
  • [2] M. G. Kendall, The advanced theory of statistics, Vol. 1, Griffin, London (1943).
  • [3] L. V. Spencer and U. Fano, Phys. Rev. 81, 464 (1951).
  • [4] P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford, at the Clarendon Press, 1947. 3d ed. MR 0023198
  • [5] J. V. Neumann, Math. Grundl. d. Quantenmechanik, Berlin, Springer, 1932.
  • [6] G. Szegö, Orthogonal polynomials, American Math. Soc. Colloquium Publications 23.
  • [7] H. Messel and H. S. Green, Phys. Rev. 87, 738 (1952).

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DOI: https://doi.org/10.1090/qam/58025
Article copyright: © Copyright 1954 American Mathematical Society

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