Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Addendum to: ``Arithmetic means of Fourier coefficients'' (Proc. Amer. Math. Soc. 55 (1976), no. 1, 83-86)


Author: Rajendra Sinha
Journal: Proc. Amer. Math. Soc. 60 (1976), 243-244
MSC: Primary 42A16
DOI: https://doi.org/10.1090/S0002-9939-1976-0420109-2
Original Article: Proc. Amer. Math. Soc. 55 (1976), 83-86.
MathSciNet review: 0420109
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let f be integrable and periodic with period 2$ 2\pi $. Then a necessary and sufficient condition for $ \tilde f$ to be equivalent to a continuous function is that $ - (1/\pi )\smallint _t^\pi (f(x + u) - f(x - u))/2\tan (u/2)\,du$ converges uniformly in x as $ t \to 0 + $.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A16

Retrieve articles in all journals with MSC: 42A16


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0420109-2
Keywords: Fourier series, conjugate function, normal family, equicontinuity
Article copyright: © Copyright 1976 American Mathematical Society