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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Then the connection between the order of $L_p$—smoothness of a $L_p$—function $\varphi$and the rate of $L_p$-convergence of these families to $\varphi$, as $\varepsilon$ tends to 0, is obtained.
📌 3 Key Takeaways
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Objective & Hypothesis:We introduce a family of Balakrishnan—Rubin-type hypersingular integrals depending ona parameter $\varepsilon$ and generated by the Gauss—Weierstrass semigroup.
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Key Findings & Data:We introduce a family of Balakrishnan—Rubin-type hypersingular integrals depending ona parameter $\varepsilon$ and generated by the Gauss—Weierstrass semigroup.
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Conclusion & Impact:Then the connection between the order of $L_p$—smoothness of a $L_p$—function $\varphi$and the rate of $L_p$-convergence of these families to $\varphi$, as $\varepsilon$ tends to 0, is obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riesz potentials · Bessel potentials · truncated hypersingular integrals
Abstract
We introduce a family of Balakrishnan—Rubin-type hypersingular integrals depending ona parameter $\varepsilon$ and generated by the Gauss—Weierstrass semigroup. Then the connection between the order of $L_p$—smoothness of a $L_p$—function $\varphi$and the rate of $L_p$-convergence of these families to $\varphi$, as $\varepsilon$ tends to 0, is obtained.
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Cite This Article
ERYİĞİT, M., ÇOBANOĞLU, S. (2017). On the rate of $L_p$-convergence of Balakrishnan—Rubin-type hypersingular integrals associated to the Gauss-Weierstrass semigroup. Turkish Journal of Mathematics, Cilt: 41 - Sayı: 6, 1376–1384. https://ajindex.com/articles/723149