Kernels of Integral Equations Can Be Boundedly Infinitely Differentiable on $\mathbb{R}^2$

Igor M. Novitskii

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arXiv · 1210.0447

Kernels of Integral Equations Can Be Boundedly Infinitely Differentiable on $\mathbb{R}^2$

Igor M. Novitskii

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Abstract

In this paper, we reduce the general linear integral equation of the third kind in $L^2(Y,\mu)$, with largely arbitrary kernel and coefficient, to an equivalent integral equation either of the second kind or of the first kind in $L^2(\mathbb{R})$, with the kernel being the linear pencil of bounded infinitely differentiable bi-Carleman kernels expandable in absolutely and uniformly convergent bilinear series. The reduction is done by using unitary equivalence transformations.

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BibTeX RIS

Igor M. Novitskii. 2012-10-01. Kernels of Integral Equations Can Be Boundedly Infinitely Differentiable on $\mathbb{R}^2$. https://arxiv.org/abs/1210.0447

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