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Abstract
We consider the generalized shift operator defined by (Shuf)(g) = ∫Gf(tut−1g)dt on a compact group G, and by using this operator, we define spherical modulus of smoothness. So, we prove Stechkin and Jackson‐type theorems.
Highlights
We prove some theorems on absolutely convergent Fourier series in the metric space L2(G), where G is a compact group
The algebra of absolutely convergent Fourier series is a subject matter about which a good deal, far from everything, is known
Like many branches of harmonic analysis on T and R, the theory of absolutely convergent Fourier series is a fruitful source of questions about the corresponding entity for compact groups
Summary
We consider the generalized shift operator defined by (Shu f )(g) = G f (tut−1g)dt on a compact group G, and by using this operator, we define “spherical” modulus of smoothness. 2000 Mathematics Subject Classification: 42C10, 43A77, 43A90
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