LAUSR

Abstract We generalize the pre-orthogonal adaptive Fourier approximation developed by T. Qian et al [11] , [9] , [5] to functions in the Bergman space on the unit disc and the unit ball to the Bergman space A 2 ( D ) on the irreducible bounded symmetric domain D . We show that A 2 ( D ) satisfies the boundary vanishing property, so that the maximum selection principle allows us to give an adaptive expansion of any function f ∈ A 2 ( D ) in terms of linear combinations of generalized kernel functions in an optimal way.