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arXiv · 2512.16840

On Some Transformations Associated to a Certain Cone

Vladimir Vasilyev·Denis Tokarev
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Abstract

A model elliptic pseudo-differential equation in $4$-faced cone is studied in Sobolev--Slobodetskii space. The Bochner kernel for such a cone is evaluated and explicit formula for unique solution to the considered equation is presented under certain restrictions on the symbol. Boundary value problem with additional integral condition is considered and unique solvability to the boundary value problem is proved.

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Vladimir Vasilyev, Denis Tokarev. 2025-12-18. On Some Transformations Associated to a Certain Cone. https://arxiv.org/abs/2512.16840

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