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In this chapter we present the \(L_{p}\) , \(p\ge 1\) , approximation properties of activated singular integral operators over the real line. We establish their approximation to the unit operator with rates. The kernels here come from neural network activation functions and we employ the related density functions. The derived inequalities use the high order \(L_{p}\) modulus of smoothness.

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Quantitative \(L_{p}\) Approximation by Activated Singular Integrals

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

In this chapter we present the \(L_{p}\) , \(p\ge 1\) , approximation properties of activated singular integral operators over the real line. We establish their approximation to the unit operator with rates. The kernels here come from neural network activation functions and we employ the related density functions. The derived inequalities use the high order \(L_{p}\) modulus of smoothness.