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

 

A model of Euclidean $ 2$-space


Author: M. S. Krishna Sastry
Journal: Proc. Amer. Math. Soc. 28 (1971), 114-118
MSC: Primary 30.81
MathSciNet review: 0284595
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Abstract: In this paper a model of Euclidean $ 2$-space, called the spin model, is introduced. To each complex-valued function $ f$ defined in an open subset of the complex plane is associated a function $ \tilde f$ mapping an open subset of the spin model space into the two-dimensional real vector space of two-rowed real column matrices. Cauchy's theorem and Cauchy's integral formula for an analytic function $ f$ are written as theorems involving the function $ \tilde f$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0284595-9
PII: S 0002-9939(1971)0284595-9
Keywords: Spin model of Euclidean $ 2$-space, Fréchet differentiable, Cauchy-Riemann operator
Article copyright: © Copyright 1971 American Mathematical Society