Analysis Mathematica
Volume/Issue:
Volume 32: Issue 1
Fejér means of  functions on noncommutative Vilenkin groups with respect to the character system
Author:
György Gát College of Nyíregyháza, Inst. of Math. and Comp. Sci. 4400 Nyíregyháza, PO.Box 166, Hungary 4400 Nyíregyháza, PO.Box 166, Hungary

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Pages:
25–48
Online Publication Date:
16 Jun 2006
Publication Date:
16 Mar 2006
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10476-006-0002-0
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Summary  

It is known that the Fejr means - with respect to the character system of the Walsh, and bounded Vilenkin groups - of an integrable function converge to the function a.e. In this work we discuss analogous problems on the complete product of finite, not necessarily Abelian groups with respect to the character system for functions that are constant on the conjugacy classes. We find that the nonabelian case differs from the commutative case. We prove the a.e. convergence of the (C,1) means of the Fourier series of square integrable functions. We also prove the existence  of a function f∊Lq  for some q >1 such that sup |σn f | = + ∞ a.e. This is a sharp contrast between the Abelian and the nonabelian cases.

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Cover Analysis Mathematica
Analysis Mathematica
Print ISSN:
0133-3852
Online ISSN:
1588-273X

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Analysis Mathematica
Language English
Size B5
Year of
Foundation		 1975
Volumes
per Year		 1
Issues
per Year		 4
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0133-3852 (Print)
ISSN 1588-273X (Online)

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