On the zeros of the slice Bergman kernels for the upper half space and the unit ball on quaternions and Clifford algebras

DOI10.1007/s11785-016-0550-7zbMath1364.30058OpenAlexW2303901964MaRDI QIDQ523041

Jong-Do Park

Publication date: 20 April 2017

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-016-0550-7

zbMATH Keywords

Bergman kernelslice regular functionsslice monogenic functions

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items

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Cites Work

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• The explicit forms and zeros of the Bergman kernel function for Hartogs type domains
• An extension theorem for slice monogenic functions and some of its consequences
• Extension results for slice regular functions of a quaternionic variable
• Further properties of the Bergman spaces of slice regular functions
• The Bergman kernel of the symmetrized polydisc in higher dimensions has zeros
• An explicit computation of the Bergman kernel function
• The Bergman kernel of the minimal ball and applications
• Explicit formulas of the Bergman kernel for 3-dimensional complex ellipsoids
• Bloch, Besov and Dirichlet spaces of slice hyperholomorphic functions
• Gleason's problem and Schur multipliers in the multivariable quaternionic setting
• The Bergman-Sce transform for slice monogenic functions
• New formulas of the Bergman kernels for complex ellipsoids in $\mathbb {C}^2$
• On Two Approaches to the Bergman Theory for Slice Regular Functions
• A note on the Bergman kernel

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