A theorem of generalized Cauchy-Pompeiu type on finite-dimensional associative algebras |
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Authors: | Herbert H. Snyder |
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Affiliation: | 1. University Extension Services, P.O. Box 1494, 22560, Tappahamock, VA, USA
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Abstract: | The author takes up the following problem: suppose given a class of regular hypercomplex functions, i.e., with domains and ranges in a finite-dimensional associative algebra (over the reals) with unity element (so that it is not, in general, a division algebra). Does there nevertheless exist for such functions an integral formula of Cauchy's type, or perhaps of Cauchy-Pompeiu tipe? The author obtains a formula of Cauchy-Pompeiu type (wich, in the commutative case, is similar to a Green identity). |
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