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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On a Bergman-Whittaker type operator in five or more variables

Author: Dean K. Kukral
Journal: Proc. Amer. Math. Soc. 39 (1973), 122-124
MSC: Primary 35C15; Secondary 35J05
MathSciNet review: 0312055
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Abstract: It is shown that there cannot exist a simple generating function for homogeneous harmonic polynomials in five or more variables similar to those known to exist for three and four variables. Thus there is no simple immediate generalization of the three dimensional Bergman-Whittaker operator (and Gilbert's four dimensional operator) to five or more dimensions.

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  • [1] David Colton, Integral operators for elliptic equations in three independent variables. I, Applicable Anal. 4 (1974/75), 77–95. MR 0445098 (56 #3443)
  • [2] David Colton, Bergman operators for elliptic equations in four independent variables, SIAM J. Math. Anal. 3 (1972), 401–412. MR 0310407 (46 #9507)
  • [3] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391 (16,426a)
  • [4] A. Erdélyi et al., Higher transcendental functions. Vol. II, McGraw-Hill, New York, 1953. MR 15, 419.
  • [5] Robert P. Gilbert, Function theoretic methods in partial differential equations, Mathematics in Science and Engineering, Vol. 54, Academic Press, New York-London, 1969. MR 0241789 (39 #3127)
  • [6] D. K. Kukral, Ph.D. Thesis, Indiana University, Bloomington, Ind., 1972.

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PII: S 0002-9939(1973)0312055-7
Article copyright: © Copyright 1973 American Mathematical Society