We describe on the Heisenberg group H_n a family of spaces M(h, X) of functions which play a role analogous to the trigonometric polynomials in T" or the functions of exponential type in R". In particular we prove that for the space M(h, X), Jackson's theorem holds in the classical form while Bernstein's inequality hold in a modified form. We end the paper with a characterization of the functions of the Lipschitz space Λ', by the behavior of their best approximations by functions in the space M(h, X).
Bernstein and Jackson theorems for the Heisenberg group
GIULINI, SAVERIO
1985-01-01
Abstract
We describe on the Heisenberg group H_n a family of spaces M(h, X) of functions which play a role analogous to the trigonometric polynomials in T" or the functions of exponential type in R". In particular we prove that for the space M(h, X), Jackson's theorem holds in the classical form while Bernstein's inequality hold in a modified form. We end the paper with a characterization of the functions of the Lipschitz space Λ', by the behavior of their best approximations by functions in the space M(h, X).
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