A Generalized Fejér’s Theorem for Locally Compact Groups
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The classical Fejér’s theorem is a criterion for pointwise convergence of Fourier series on the unit circle. We generalize it to locally compact groups.
KeywordsFourier series Fejér’s theorem Approximate identity Pointwise convergence
Mathematics Subject ClassificationPrimary 43A07 Secondary 42B05 40A05
Most of the paper was completed when I was doing my postdoctoral research supported by ERC Advanced Grant No. 267079. I would like to express my gratitude to my mentor Joachim Cuntz. Part of the paper is carried out during a visit to Besançon. I thank Quanhua Xu for his invitation and hospitality, and Simeng Wang for his help. I thank Loukas Grafakos for answering questions raised by me on reading his excellent GTM book: Classical Fourier Analysis. I thank Stefan Cobzas and Ferenc Weisz for their helpful discussions and comments. Finally thanks are due to the referee and the editor for valuable suggestions which greatly improve readability of the paper.
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