Proceedings of the American Mathematical Society

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On the Cauchy problem of the differential operator $ S\mu $


Author: W. Y. Lee
Journal: Proc. Amer. Math. Soc. 51 (1975), 149-154
MSC: Primary 35G10
MathSciNet review: 0369892
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Abstract: 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.


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  • [1] 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.
  • [2] I. M. Gel′fand and G. E. Shilov, Generalized functions. Vol. 3, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1967 [1977]. Theory of differential equations; Translated from the Russian by Meinhard E. Mayer. MR 0435833
  • [3] 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 0077616
  • [4] W. Y. Lee, The space of type $ {H_\mu }$ and their Hankel transformations, Ph.D. Thesis, SUNY at Stony Brook, 1971.
  • [5] L. Schwartz, Théorie des distributions. Vols. 1, 2, Actualités Sci. Indust., nos. 1091, 1122, Hermann, Paris, 1950, 1951. MR 12, 31; 833.
  • [6] E. C. Titchmarsh, Han-shu lun, Translated from the English by Wu Chin, Science Press, Peking, 1964 (Chinese). MR 0197687
  • [7] François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
  • [8] A. H. Zemanian, A distributional Hankel transformation, SIAM J. Appl. Math. 14 (1966), 561–576. MR 0201930
  • [9] A. H. Zemanian, Hankel transforms of arbitrary order, Duke Math. J. 34 (1967), 761–769. MR 0223836
  • [10] A. H. Zemanian, The Hankel transformation of certain distributions of rapid growth, SIAM J. Appl. Math. 14 (1966), 678–690. MR 0211211
  • [11] A. H. Zemanian, Generalized integral transformations, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1968. Pure and Applied Mathematics, Vol. XVIII. MR 0423007
  • [12] A. H. Zemanian, Distribution theory and transform analysis. An introduction to generalized functions, with applications, McGraw-Hill Book Co., New York-Toronto-London-Sydney, 1965. MR 0177293
  • [13] L. Hörmander, Linear partial differential operators, Die Grundlehren der math. Wissenschaften, Band 116, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #4221.
  • [14] E. L. Koh, The Hankel transformation of negative order for distributions of rapid growth, SIAM J. Math. Anal. 1 (1970), 322–327. MR 0267395

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0369892-4
Keywords: Cauchy problem, differential operator $ {S_\mu }$, Hankel transformation, reduced order, Phragmén-Lindelöf theorem
Article copyright: © Copyright 1975 American Mathematical Society