References
Bochner, S. and Martin, W. T.,Several Complex Variables Princeton University Press, 1948.
Hausdorff, F.,Zur Theorie der Systeme complexer Zahlen, Leipz. Ber., vol. 52 (1900), pp. 43–61.
Portmann, W. O.,A derivative for Hausdorff-analytic functions, Proc. Am. Math. Soc. V. 10 (1959), pp. 101–105.
Rinehart, R. F.,The equivalence of definitions of a matric function, Am. Math. Monthly V. 62, pp. 395–414.
Rinehart, R. F.,Extension of the derivative concept for functions of matrices, Proc. Am. Math. Soc. V. 8 (1957), pp. 329–335.
Rinehart, R. F.,Elements of a theory of intrinsic functions on algebras, Duke Math. Jour. V. 27 (1960), pp. 1–20.
Ringleb, F.,Beiträge zur Funktionentheorie in hyperkomplexen Systemen, I., Rend. d. Circ. Mat. di Palermo, V. 57 (1933), pp. 311–340.
Trampus, A.,Differentiability and Analyticity of Functions in Linear Algebras, Duke Math. Jour. V. 27 (1960), pp. 431–442.
Wagner, R. W.,Differentials and analytic continuation in non commutative algebras, Duke Math. Jour. V. 9 (1942), pp. 677–691.
Wagner, R. D.,The generalized Laplace equations in a function theory for commutative algebras, Duke Math. Jour., V. 15 (1948), pp. 455–461.
Rinehart, R. F. and Wilson, J. C.,Differentiability and continuity of functions on algebras, Proc. Am. Math. Soc. V 14 (1963).
Author information
Authors and Affiliations
Additional information
Supported by ONR grant.
Rights and permissions
About this article
Cite this article
Rinehart, R.F., Wilson, J.C. Two types of Differentiability of functions on Algebras. Rend. Circ. Mat. Palermo 11, 204–216 (1962). https://doi.org/10.1007/BF02843955
Issue Date:
DOI: https://doi.org/10.1007/BF02843955