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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the Cauchy problem of the differential operator $S\mu$
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by W. Y. Lee PDF
Proc. Amer. Math. Soc. 51 (1975), 149-154 Request permission


I. M. Gelfand and G. E. Shilov have obtained the uniqueness and correctness class of the Cauchy problem of the differential operator $i(\partial /\partial x)$. If ${S_\mu }$ is some particular differential operator, then the uniqueness class of the differential operator ${S_\mu }$ is given in this paper.
    I. M. Gel’fand and G. E. Šilov, Generalized functions. Vol. 2: Spaces of fundamental functions, Fizmatgiz, Moscow, 1958; English transl., Academic Press; Gordon and Breach, New York, 1968. MR 21 #5142a; 37 #5693.
  • I. M. Gel′fand and G. E. Shilov, Generalized functions. Vol. 1, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1964 [1977]. Properties and operations; Translated from the Russian by Eugene Saletan. MR 0435831
  • James L. Griffith, Hankel transforms of functions zero outside a finite interval, J. Proc. Roy. Soc. New South Wales 89 (1955), 109–115 (1956). MR 77616
  • W. Y. Lee, The space of type ${H_\mu }$ and their Hankel transformations, Ph.D. Thesis, SUNY at Stony Brook, 1971. L. Schwartz, ThĂ©orie des distributions. Vols. 1, 2, ActualitĂ©s Sci. Indust., nos. 1091, 1122, Hermann, Paris, 1950, 1951. MR 12, 31; 833.
  • E. C. Titchmarsh, Han-shu lun, Science Press, Peking, 1964 (Chinese). Translated from the English by Wu Chin. MR 0197687
  • François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
  • A. H. Zemanian, A distributional Hankel transformation, SIAM J. Appl. Math. 14 (1966), 561–576. MR 201930, DOI 10.1137/0114049
  • A. H. Zemanian, Hankel transforms of arbitrary order, Duke Math. J. 34 (1967), 761–769. MR 223836, DOI 10.1215/S0012-7094-67-03479-5
  • A. H. Zemanian, The Hankel transformation of certain distributions of rapid growth, SIAM J. Appl. Math. 14 (1966), 678–690. MR 211211, DOI 10.1137/0114056
  • A. H. Zemanian, Generalized integral transformations, Pure and Applied Mathematics, Vol. XVIII, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1968. MR 0423007
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  • L. Hörmander, Linear partial differential operators, Die Grundlehren der math. Wissenschaften, Band 116, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #4221.
  • E. L. Koh, The Hankel transformation of negative order for distributions of rapid growth, SIAM J. Math. Anal. 1 (1970), 322–327. MR 267395, DOI 10.1137/0501028
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 149-154
  • MSC: Primary 35G10
  • DOI:
  • MathSciNet review: 0369892