Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Differentiable intrinsic functions of complex matrices


Author: R. F. Rinehart
Journal: Proc. Amer. Math. Soc. 12 (1961), 565-573
MSC: Primary 30.83
DOI: https://doi.org/10.1090/S0002-9939-1961-0155001-3
MathSciNet review: 0155001
Full-text PDF

References | Similar Articles | Additional Information

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

  • [1] S. Bochner and W. T. Martin, Several complex variables, Princeton University Press, 1948. MR 0027863 (10:366a)
  • [2] F. Hausdorff, Zur Theorie der Systeme complexer Zahlen, Leipziger Berichte vol. 52 (1900) pp. 43-61.
  • [3] W. O. Portmann, A derivative for Hausdorff-analytic functions, Proc. Amer. Math. Soc. vol. 10 (1959) pp. 101-105. MR 0106989 (21:5718)
  • [4] R. F. Rinehart, The equivalence of definitions of a matric function, Amer. Math. Monthly vol. 62 (1955) pp. 395-414. MR 0069908 (16:1099e)
  • [5] -, Extension of the derivative concept for functions of matrices, Proc. Amer. Math. Soc. vol. 8 (1957) pp. 329-335. MR 0084564 (18:882c)
  • [6] -, Elements of a theory of intrinsic functions on algebras, Duke Math. J. vol. 27 (1960) pp. 1-19. MR 0120349 (22:11104)
  • [7] -, Intrinsic functions on matrices, Duke Math. J. vol. 28 (1961) pp. 291-300. MR 0155000 (27:4942)
  • [8] F. Ringleb, Beiträge zur Funktionentheorie in hyperkomplexen Systemen. I, Rend. Circ. Mat. Palermo vol. 57 (1933) pp. 311-340.
  • [9] K. Shoda, Ein Kriterium für normale einfache hyperkomplexen Systeme, Proc. Imp. Acad. Japan, Tokyo vol. 10 (1934) pp. 195-197. MR 1568372
  • [10] E. C. Titchmarsh, The theory of functions, Oxford University Press, 1947.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30.83

Retrieve articles in all journals with MSC: 30.83


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1961-0155001-3
Article copyright: © Copyright 1961 American Mathematical Society

American Mathematical Society