Estimates of n-widths of Sobolev's classes on compact globally symmetric spaces of rank one

Approximation of smooth functions on compact two-point homogeneous spaces

“…where the last inequalities in (4.8) and (4.9) are contained in [BKLT,Theorem 1]. It remains to prove the lower estimates for 1 q p ∞.…”

On the Problem of Optimal Reconstruction

“…As regards the first part of the problem, in many cases, its solution has its roots in the theory of N -widths. Estimates of N -widths of Sobolev's classes on two point homogeneous spaces (in particular, on S 2 ) have been found in [1,2,18,19,21,22,26]. In Section 3 we obtain lower bounds for linear and Alexandrov cowidths which give, in particular, lower bounds for…”

“…Let V and W be any convex symmetric bodies in R n , V ⊂ B n (2) , then for any n ∈ N and > 0 there is such µ ∈ (0, 1) that in any subspace L m ⊂ R n , dim L m ≥ µ n there exists such α * ∈ L m that…”

“…Since n = dim ⊕ m k=0 H k m d (see, e.g., [2]), then from the Bernstein inequality (3.17) and (3.16) we obtain…”

Núcleos isotrópicos e positivos definidos sobre espaços 2-homogêneos

“…Os elementos da base S d k,a são comumente chamados de harmônicos esféricos. Mais informações sobre a Fórmula de Adição, sua aplicabilidade e sobre a análise harmônica em geral atrelada aos espaços M d podem ser encontradas em [8,9,28,36] e nas referências lá citadas.…”