Ligocka, Ewa 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 Ann. Pol. Math. 71, No. 2, 151-160 (1999). 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 Keywords:harmonic function; harmonic polynomials; spherical harmonics; conjugate harmonic function PDFBibTeX XMLCite \textit{E. Ligocka}, Ann. Pol. Math. 71, No. 2, 151--160 (1999; Zbl 0936.31005) Full Text: DOI