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Registration Number

0226U000875, (0124U003931) , R & D reports

Title

Pseudo-Differential Equations over Non-Archimedean Fields

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Неархімедове перетворення Кельвіна. Неархімедова задача Неймана.

Head

Kochubei Anatolii N., Доктор фізико-математичних наук

Registration Date

17-01-2026

Organization

Institute of Mathematics of the National Academy of Sciences of Ukraine

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To develop a theory of pseudo-differential equations for real and complex-valued functions on non-Archimedean spaces, including probabilistic interpretations of objects of this theory, to a level comparable to the contemporary state of the theory of classical equations of mathematical physics.

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We have defined and studied a non-Archimedean Kelvin transformation. This is based on a new approach using the notion of an unramified extension of a local field. These results can be used to construct alpha-harmonic functions associated with the Vladimirov-Taibleson operator. We proved theorems of existence and uniqueness of solutions of the non-Archimedean Neumann problem.We studied the Vladimirov-Taibleson type operator on a model set with nontrivial boundary, the multiplicative group of a local field.

Product Description

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Anatoly Kochubei
Mariia V. Serdiuk

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2026-01-17