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Reproducing kernels for holomorphic functions on some balls related to the Lie ball

Keiko Fujita (2007)

Annales Polonici Mathematici

We consider holomorphic functions and complex harmonic functions on some balls, including the complex Euclidean ball, the Lie ball and the dual Lie ball. After reviewing some results on Bergman kernels and harmonic Bergman kernels for these balls, we consider harmonic continuation of complex harmonic functions on these balls by using harmonic Bergman kernels. We also study Szegő kernels and harmonic Szegő kernels for these balls.

Restricted interpolation by meromorphic inner functions

Alexei Poltoratski, Rishika Rupam (2016)

Concrete Operators

Meromorphic Inner Functions (MIFs) on the upper half plane play an important role in applications to spectral problems for differential operators. In this paper, we survey some recent results concerning function theoretic properties of MIFs and show their connections with spectral problems for the Schrödinger operator.

Riemann problem on the double of a multiply connected circular region

V. V. Mityushev (1997)

Annales Polonici Mathematici

The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.

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