Properties of Complete Orthonormal Systems on Matrix Spaces

摘要

In this paper properties of complete orthonormal systems on the domain D in the 2 x 2 and n x n cases were studied. The domain D is one of four main types of irreducible bounded symmetric domains given by E. Cartan. The discussion includes inequalities for polynomials on matrix spaces, equisummability of real complete orthonormal systems on the unitary group of order 2, and Harnack's theorems on matrix spaces.