Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1975-0369892-4
MathSciNet review: 0369892
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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

  • [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] -, Generalized functions. Vol. 3: Some questions on the theory of differential equations, Fizmatgiz, Moscow, 1958; English transl., Academic Press, New York, 1967. MR 21 #5142b; 36 #506. MR 0435833 (55:8786c)
  • [3] J. L. Griffith, Hankel transforms of functions zero outside a finite interval, J. Proc. Roy. Soc. New South Wales 89 (1955), 109-115 (1956). MR 17, 1066. MR 0077616 (17:1066d)
  • [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, The theory of functions, Oxford Univ. Press, London, 1964. MR 0197687 (33:5850)
  • [7] F. Treves, Topological vector spaces. Distributions and kernels, Academic Press, New York, 1967. MR 37 #726. MR 0225131 (37:726)
  • [8] A. H. Zemanian, A distributional Hankel transformation, J. SIAM Appl. Math. 14 (1966), 561-576. MR 34 #1807. MR 0201930 (34:1807)
  • [9] -, Hankel transforms of arbitrary order, Duke Math. J. 34 (1967), 761-769. MR 36 #6883. MR 0223836 (36:6883)
  • [10] -, The Hankel transformation of certain distributions of rapid growth, J. SIAM Appl. Math. 14 (1966), 678-690. MR 35 #2093. MR 0211211 (35:2093)
  • [11] A. H. Zemanian, Generalized integral transformations, Interscience, New York, 1968. MR 0423007 (54:10991)
  • [12] -, Distribution theory and transform analysis. An introduction to generalized functions, with applications, Internat. Series in Pure and Appl. Math., McGraw-Hill, New York, 1965. MR 31 #1556. MR 0177293 (31:1556)
  • [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 42 #2297. MR 0267395 (42:2297)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35G10

Retrieve articles in all journals with MSC: 35G10


Additional Information

DOI: https://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

American Mathematical Society