2010
DOI: 10.4171/zaa/1420
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On the Point Behavior of Fourier Series and Conjugate Series

Abstract: We investigate the point behavior of periodic functions and Schwartz distributions when the Fourier series and the conjugate series are both Abel summable at a point. In particular we show that if f is a bounded function and its Fourier series and conjugate series are Abel summable to values γ and β at the point θ_0 … Show more

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Cited by 9 publications
(7 citation statements)
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“…[19]). Recent applications to the theory of Fourier and conjugate series are considered in [6]. We also mention that the results of this article are closely related to those from [7,24], though with a different approach.…”
Section: Introductionmentioning
confidence: 78%
“…[19]). Recent applications to the theory of Fourier and conjugate series are considered in [6]. We also mention that the results of this article are closely related to those from [7,24], though with a different approach.…”
Section: Introductionmentioning
confidence: 78%
“…Other related results are found in [23,24,27]. Some Tauberian results for distributions have interesting consequences in the theory of Fourier series [11].…”
Section: Introductionmentioning
confidence: 83%
“…Under additional assumptions on the growth order of f at ±∞, it is possible to establish a more precise link between the order of summability β and the order of the symmetric point value [20]. We refer to [5,6,7,16,18,20] for studies about the interplay between local behavior of distributions and summability of series and integrals. We now proceed to show our main result.…”
Section: Resultsmentioning
confidence: 99%