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.
- 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
M. G. Kendall, The advanced theory of statistics, Vol. 1, Griffin, London (1943).
L. V. Spencer and U. Fano, Phys. Rev. 81, 464 (1951).
- P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford, at the Clarendon Press, 1947. 3d ed. MR 0023198
J. V. Neumann, Math. Grundl. d. Quantenmechanik, Berlin, Springer, 1932.
G. Szegö, Orthogonal polynomials, American Math. Soc. Colloquium Publications 23.
H. Messel and H. S. Green, Phys. Rev. 87, 738 (1952).
J. A. Shohat and J. D. Tamarkin, The problem of moments, American Math. Soc., Mathematical Surveys 1 (1943).
M. G. Kendall, The advanced theory of statistics, Vol. 1, Griffin, London (1943).
L. V. Spencer and U. Fano, Phys. Rev. 81, 464 (1951).
P. A. M. Dirac, The principles of quantum mechanics, Oxford, Clarendon Press (1947).
J. V. Neumann, Math. Grundl. d. Quantenmechanik, Berlin, Springer, 1932.
G. Szegö, Orthogonal polynomials, American Math. Soc. Colloquium Publications 23.
H. Messel and H. S. Green, Phys. Rev. 87, 738 (1952).
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Article copyright:
© Copyright 1954
American Mathematical Society
