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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$.

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

  • [1] W. F. Eberlein, The spin model of Euclidean $ 3$-space, Amer. Math. Monthly 69 (1962), 587-598. MR 1531766
  • [2] -, Cauchy-Riemann operator, Amer. J. Phys. 35 (1967), 53.
  • [3] S. Saks and A. Zygmund, Analytic functions, 2nd ed., Monografie Mat., Tom 28, PWN, Warsaw, 1965. MR 31 #4889. MR 0055432 (14:1073a)

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Keywords: Spin model of Euclidean $ 2$-space, Fréchet differentiable, Cauchy-Riemann operator
Article copyright: © Copyright 1971 American Mathematical Society

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