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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References | Similar Articles | Additional Information

**[1]**S. Bergman,*The kernel function and conformal mapping*, Mathematical Surveys, vol. 5, American Mathematical Society, 1950. MR**0038439 (12:402a)****[2]**S. Bochner,*Group invariance of Cauchy's formula in several variables*, Ann. of Math. vol. 45 (1944) pp. 686-707. MR**0011131 (6:123i)****[3]**L. K. Hua,*On the theory of functions of several complex variables*. I.*On a complete orthonormal system in the hyperbolic space of rectangular matrices*, Dokl. Akad. Nauk SSSR (N.S.) vol. 93 (1953) pp. 775-777 [Math. Rev. 15 (1954) p. 617] and J. Chinese Math. Soc. vol. 2 (1953) pp. 288-323 [Math. Rev. 17, 1956, p. 191]. MR**0060035 (15:617a)****[4]**-,*Harmonic analysis of the classical domain in the study of analytic functions of several complex variables*, Mimeographed Lecture Notes, about 1956.**[5]**J. Mitchell,*An example of a complete orthonormal system and the kernel function in the geometry of matrices*, Proceedings of Second Canadian Mathematical Congress, Vancouver, 1949, pp. 155-163. MR**0043916 (13:339c)****[6]**-,*The kernel function in the geometry of matrices*, Duke Math. J. vol. 19 (1952) pp. 575-584. MR**0050690 (14:368b)****[7]**-,*Potential theory in the geometry of matrices*, Trans. Amer. Math. Soc. vol. 79 (1955) pp. 401-422. MR**0072242 (17:253a)****[8]**E. T. Whittaker and G. N. Watson,*A course of modern analysis*, Cambridge, Cambridge University Press, 1948. MR**1424469 (97k:01072)**

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

Article copyright:
© Copyright 1959
American Mathematical Society