On a Bergman-Whittaker type operator in five or more variables
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- by Dean K. Kukral PDF
- Proc. Amer. Math. Soc. 39 (1973), 122-124 Request permission
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
- David Colton, Integral operators for elliptic equations in three independent variables. I, Applicable Anal. 4 (1974/75), 77–95. MR 445098, DOI 10.1080/00036817408839084
- David Colton, Bergman operators for elliptic equations in four independent variables, SIAM J. Math. Anal. 3 (1972), 401–412. MR 310407, DOI 10.1137/0503038
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391 A. Erdélyi et al., Higher transcendental functions. Vol. II, McGraw-Hill, New York, 1953. MR 15, 419.
- 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 D. K. Kukral, Ph.D. Thesis, Indiana University, Bloomington, Ind., 1972.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 122-124
- MSC: Primary 35C15; Secondary 35J05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312055-7
- MathSciNet review: 0312055