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Proceedings of the American Mathematical Society
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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.


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

  • [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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0312055-7
PII: S 0002-9939(1973)0312055-7
Article copyright: © Copyright 1973 American Mathematical Society