Abstract

MARTINEZ-GUZMAN, Gerardo; LORANCA, María Beatríz Bernábe; GOMEZ, Mariano Larios  and  VANOYE, Jorge Ruiz. Trigonometric approximation in Lipschitz spaces. Rev. Mat [online]. 2022, vol.29, n.1, pp.39-52. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v29i1.45440.

The approximation by generalized trigonometric polynomials for Lipschitz defined functions in certain groups depends on some properties of the group defined metric. Metrics which allow this approximation are called Lipschitz compatible. In this work we give for certain class of groups, conditions under which Lipschitz compatible metrics are boundedly equivalent, i.e., they generate the same Lipschitz space. In particular, for the multiplicative group of modulus one complex numbers the conditions are necessary and sufficient for the compatible Lipschitz metrics to be boundedly equivalent.

Keywords : Lipschitz spaces; invariant metrics; trigonometric polynomials; topological groups; dual space..

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