A model of Euclidean $2$-space
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- by M. S. Krishna Sastry PDF
- Proc. Amer. Math. Soc. 28 (1971), 114-118 Request permission
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
- W. F. Eberlein, The Spin Model of Euclidean 3-Space, Amer. Math. Monthly 69 (1962), no. 7, 587–598. MR 1531766, DOI 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
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 114-118
- MSC: Primary 30.81
- DOI: https://doi.org/10.1090/S0002-9939-1971-0284595-9
- MathSciNet review: 0284595