Keywords
invariant metrics
trigonometric polynomials
topological groups
dual space
espacios de Lipschitz
métricas invariantes
polinomios trigonométricos
grupos topológicos
espacio dual
How to Cite
Abstract
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.
References
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