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On a uniqueness problem in the theory of linear integral equations


Author: Robert R. Stevens
Journal: Proc. Amer. Math. Soc. 49 (1975), 95-103
MSC: Primary 45A05; Secondary 26A42
DOI: https://doi.org/10.1090/S0002-9939-1975-0387987-6
MathSciNet review: 0387987
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Abstract: The primary purpose of this paper is to give sufficient conditions for a function $ G$ which ensure that if $ \int_0^1 {f(xt)G(t)dt = 0} $ a.e. in $ (0, 1)$ then the function $ f$ is zero almost everywhere in $ (0, 1)$. Several applications are given.


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  • [1] M. A. Evgrafov, Analytic functions, ``Nauka", Moscow, 1965; English transl., Saunders, Philadelphia, Pa., 1966. MR 32 #5843; 33 #5849. MR 0197686 (33:5849)
  • [2] E. W. Hobson, The theory of functions of a real variable and the theory of Fourier series. Vols. I, II, Cambridge Univ. Press, New York, 1927; reprint, Dover, New York, 1958. MR 19, 1166.
  • [3] H. L. Royden, Real analysis, 2nd ed., Macmillan, New York, 1969. MR 27 #1540. MR 0151555 (27:1540)
  • [4] G. Sansone and J. Gerretsen, Lectures on the theory of functions of a complex variable. Vol. I. Holomorphic functions, Noordhoff, Groningen, 1960. MR 22 #4819. MR 0113988 (22:4819)
  • [5] M. Urabe, Potential forces which yield periodic motions of a fixed period, J. Math. Mech. 10 (1961), 569-578. MR 23 #A391. MR 0123060 (23:A391)
  • [6] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Univ. Press, New York, 1966. MR 1349110 (96i:33010)
  • [7] E. T. Whittaker and G. N. Watson, A course of modern analysis. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, 4th ed., reprinted, Cambridge Univ. Press, New York, 1962. MR 31 #2375. MR 0178117 (31:2375)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0387987-6
Article copyright: © Copyright 1975 American Mathematical Society

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