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

摘要

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 Aλ2(D) and the weighted Bergman–Sobolev space A2,λ,l(D). For 0<ρ<1 we obtain exact values of the Gel'fand and linear N-widths of A2,λ,l(D) in C(ρΣ). We also obtain the Bernstein N-widths of the Hardy–Sobolev space H∞,l(D) in Aλ2(ρD).