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arXiv · 2003.04982

On a hyper-singular equation

Alexander G. Ramm
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Abstract

The equation $v=v_0+\int_0^t(t-s)^{\lambda -1}v(s)ds$ is considered, $\lambda\neq 0,-1,-2...$ and $v_0$ is a smooth function rapidly decaying with all its derivatives. It is proved that the solution to this equation does exist, is unique and is smoother than the singular function $t^{-\frac 5 4}$.

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Alexander G. Ramm. 2020-03-01. On a hyper-singular equation. https://arxiv.org/abs/2003.04982

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