A model of Euclidean -space
Abstract: In this paper a model of Euclidean -space, called the spin model, is introduced. To each complex-valued function defined in an open subset of the complex plane is associated a function 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 are written as theorems involving the function .
-  W. F. Eberlein, The Spin Model of Euclidean 3-Space, Amer. Math. Monthly 69 (1962), no. 7, 587–598. MR 1531766, https://doi.org/10.2307/2310821
-  -, Cauchy-Riemann operator, Amer. J. Phys. 35 (1967), 53.
-  Stanisław Saks and Antoni Zygmund, Analytic functions, Monografie Matematyczne, Tom XXVIII, Polskie Towarzystwo Matematyczne, Warszawa-Wroclaw, 1952. Translated by E. J. Scott. MR 0055432
- W. F. Eberlein, The spin model of Euclidean -space, Amer. Math. Monthly 69 (1962), 587-598. MR 1531766
- -, Cauchy-Riemann operator, Amer. J. Phys. 35 (1967), 53.
- 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 -space, Fréchet differentiable, Cauchy-Riemann operator
Article copyright: © Copyright 1971 American Mathematical Society