2014
DOI: 10.1007/s00041-014-9339-0
|View full text |Cite
|
Sign up to set email alerts
|

On Fourier Re-Expansions

Abstract: We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2014
2014
2021
2021

Publication Types

Select...
3
2
1

Relationship

2
4

Authors

Journals

citations
Cited by 6 publications
(2 citation statements)
references
References 18 publications
0
2
0
Order By: Relevance
“…Concerning the second sum in (15), it can be represented in an equivalent form due to the mean zero property (S 0 = 0):…”
Section: Elijah Liflyandmentioning
confidence: 99%
“…Concerning the second sum in (15), it can be represented in an equivalent form due to the mean zero property (S 0 = 0):…”
Section: Elijah Liflyandmentioning
confidence: 99%
“…In [Lif14], a similar problem of the integrability of the re-expansion for Fourier transforms of functions defined on R + = [0, ∞) has been studied. Surprisingly, necessary and sufficient conditions in terms of the membership of the sine or cosine Fourier transform in a certain Hardy space have been found.…”
Section: Introductionmentioning
confidence: 99%