One-Dimensional Fourier Transforms

Weisz, Ferenc

doi:10.1007/978-3-319-56814-0_2

Cited by 1 publication

(1 citation statement)

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“…The Bochner-Riesz summation is a technique that involves the summation of many Fourier series in a spherical manner. The first exploration of this technique was conducted by Fefferman [3] and [5]. Understanding the behavior of functions in different situations is crucial when it comes to summarizing them.…”

Section: Overview Of Bochner-riesz Summability and Its Importancementioning

confidence: 99%

Bochner-Riesz Summability Below the Critical Index: Applications and Sharp Estimates

Abdullahi Saleh,

Waheed Tariq

2023

Swb

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This research paper investigates the realm of Bochner-Riesz summability in two dimensions, providing distinct results and insights on the convergence properties of Fourier series. More precisely, the study examines the convergence properties of Fourier series. This article establishes two significant theorems: Theorem 4.1.1 offers proof that the Bochner-Riesz operator in 𝐿 2 (ℝ 2 ) is bounded for a certain multiplier function. However, this claim is contingent upon a crucial criterion. Theorem 4.1.2 presents precise estimates that indicate the logarithmic dependence on certain parameters and highlight the intricate behavior of the operator. These theorems have potential applications in signal processing and imaging, and they also serve as a solid foundation for comprehending harmonic analysis and singular integral operators. The last portion of the paper has some suggestions for further investigation. The proposals include doing research on higher dimensions, investigating the impact of additional variables, and exploring practical applications in real-world scenarios.

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Section: Overview Of Bochner-riesz Summability and Its Importancementioning

confidence: 99%