The N-widths of spaces of holomorphic functions on bounded symmetric domains, II

Abstract

Let D be a bounded symmetric domain and Σ be the Shilov boundary of D. For λ∈ W, the Wallach set, and a nonnegative integer l, we study the weighted Bergman space A λ 2( D) and the weighted Bergman–Sobolev space A 2, λ, l ( D). For 0< ρ<1 we obtain exact values of the Gel'fand and linear N-widths of A 2, λ, l ( D) in C( ρΣ). We also obtain the Bernstein N-widths of the Hardy–Sobolev space H ∞, l ( D) in A λ 2( ρD).