Abstract:
We consider some questions about the approximation of functions
on the infinite-dimensional torus by trigonometric polynomials. Our main results
are analogues of the direct and inverse theorems in the classical theory
of approximation of periodic functions and a description of the Lipschitz
spaces on the infinite-dimensional torus in terms of the best approximation.
Keywords:Lipschitz spaces, infinite-dimensional torus, harmonic analysis on compact groups,
approximation of functions, function spaces.
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