Analysis and applications of holomorphic functions in higher dimensions
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- by R. Z. Yeh
- Trans. Amer. Math. Soc. 345 (1994), 151-177
- DOI: https://doi.org/10.1090/S0002-9947-1994-1260207-2
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Erratum: Trans. Amer. Math. Soc. 347 (1995), 1081.
Abstract:
Holomorphic functions in ${R^n}$ are defined to generalize those in ${R^2}$. A Taylor formula and a Cauchy integral formula are presented. An application of the Taylor formula to the kernel of the Cauchy integral formula results in Taylor series expansions of holomorphic functions. Real harmonic functions are expanded in series of homogeneous harmonic polynomials.References
- R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 2, Wiley-Interscience, New York, 1962.
- Richard Delanghe, On regular-analytic functions with values in a Clifford algebra, Math. Ann. 185 (1970), 91–111. MR 265618, DOI 10.1007/BF01359699
- William Feller, An introduction to probability theory and its applications. Vol. I, 3rd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0228020
- W. K. Hayman, Power series expansions for harmonic functions, Bull. London Math. Soc. 2 (1970), 152–158. MR 267114, DOI 10.1112/blms/2.2.152
- Gerald N. Hile, Representations of solutions of a special class of first order systems, J. Differential Equations 25 (1977), no. 3, 410–424. MR 499218, DOI 10.1016/0022-0396(77)90054-7
- Gerald N. Hile and Pertti Lounesto, Matrix representations of Clifford algebras, Linear Algebra Appl. 128 (1990), 51–63. MR 1049072, DOI 10.1016/0024-3795(90)90282-H
- R. Z. Yeh, Hyperholomorphic functions and higher order partial differential equations in the plane, Pacific J. Math. 142 (1990), no. 2, 379–399. MR 1042052
- R. Z. Yeh, Solutions of polyharmonic Dirichlet problems derived from general solutions in the plane, J. Math. Anal. Appl. 154 (1991), no. 2, 341–363. MR 1088636, DOI 10.1016/0022-247X(91)90042-X
- R. Z. Yeh, Hyperholomorphic functions and second order partial differential equations in $\textbf {R}^n$, Trans. Amer. Math. Soc. 325 (1991), no. 1, 287–318. MR 1015927, DOI 10.1090/S0002-9947-1991-1015927-9
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 345 (1994), 151-177
- MSC: Primary 26E05; Secondary 30G35, 31B05, 35C10, 35J99
- DOI: https://doi.org/10.1090/S0002-9947-1994-1260207-2
- MathSciNet review: 1260207