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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.
📌 3 Key Takeaways
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Objective & Hypothesis:The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution.
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Key Findings & Data:The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution.
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Conclusion & Impact:Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Wiener Tauberian theorem · Paley-Wiener theorem · convolution
Abstract
The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.
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Cite This Article
CASTRO, L. P. D., GUERRA, R. C., TUAN, N. M. (2019). On Wiener's Tauberian theorems and convolution for oscillatory integral operators. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1124–1147. https://ajindex.com/articles/185543