Geodesic
Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces
Izvestiya. Mathematics , Tome 82 (2018) no. 1, pp. 186-211

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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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     author = {S. S. Platonov},
     title = {Certain approximation problems for functions on the infinite-dimensional torus: {Lipschitz} spaces},
     journal = {Izvestiya. Mathematics },
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_1_a6/}
}
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S. S. Platonov. Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces. Izvestiya. Mathematics , Tome 82 (2018) no. 1, pp. 186-211. http://geodesic.mathdoc.fr/item/IM2_2018_82_1_a6/