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On the Hartogs-type series for harmonic functions on Hartogs domains in \(\mathbb{R}^n \times \mathbb{R}^m\), \(m\geq 2\). (English) Zbl 0936.31005

The author studies series expansions for harmonic functions on Hartogs domains in \(\mathbb R^n \times \mathbb R^m\). The expansions are analogous to Hartogs series for holomorphic functions and involve an orthonormal basis in the space of spherical harmonics with coefficients that satisfy a singular differential equation. The paper contains applications to conjugate harmonic functions and the space of square integrable functions.

MSC:

31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
42C15 General harmonic expansions, frames
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