Characterization of holomorphic functions by zero spherical means

N. P. Volchkova   ; V. V. Volchkov

Matematičeskie trudy, Tome 27 (2024) no. 2, pp. 40-61

Résumé

The paper continues to study the holomorphicity problem of a function having zero contour integrals over circles. The case is considered when function $f$ is given in a ball of $\mathbb{C}^n$ with a punctured center, and integration is carried out over all spheres of two fixed radii lying in this punctured ball $\mathcal{D}$. It is established that if $f\in C^{\infty}(\mathcal{D})$, then under certain conditions for radii and certain sizes of $\mathcal{D}$ it can be concluded that the holomorphicity of the function $f$. It is shown that these requirements cannot be weakened in the general case.

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