A complete orthonormal system of homogeneous polynomials on matrix spaces of order 2

Author:
Josephine Mitchell

Journal:
Proc. Amer. Math. Soc. **10** (1959), 399-406

MSC:
Primary 32.00

DOI:
https://doi.org/10.1090/S0002-9939-1959-0105513-4

MathSciNet review:
0105513

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**[1]**Stefan Bergman,*The Kernel Function and Conformal Mapping*, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR**0038439****[2]**S. Bochner,*Group invariance of Cauchy’s formula in several variables*, Ann. of Math. (2)**45**(1944), 686–707. MR**0011131**, https://doi.org/10.2307/1969297**[3]**Lo-Kèn Hua,*On the theory of functions of several complex variables. I. On a complete orthonormal system in the hyperbolic space of rectangular matrices*, Doklady Akad. Nauk SSSR (N.S.)**93**(1953), 775–777 (Russian). MR**0060035****[4]**-,*Harmonic analysis of the classical domain in the study of analytic functions of several complex variables*, Mimeographed Lecture Notes, about 1956.**[5]**Josephine Mitchell,*An example of a complete ortho-normal system and the kernel function in the geometry of matrices*, Proc. Second Canadian Math. Congress, Vancouver, 1949, University of Toronto Press, Toronto, 1951, pp. 155–163. MR**0043916****[6]**Josephine Mitchell,*The kernel function in the geometry of matrices*, Duke Math. J.**19**(1952), 575–583. MR**0050690****[7]**Josephine Mitchell,*Potential theory in the geometry of matrices*, Trans. Amer. Math. Soc.**79**(1955), 401–422. MR**0072242**, https://doi.org/10.1090/S0002-9947-1955-0072242-6**[8]**E. T. Whittaker and G. N. Watson,*A course of modern analysis*, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR**1424469**

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DOI:
https://doi.org/10.1090/S0002-9939-1959-0105513-4

Article copyright:
© Copyright 1959
American Mathematical Society