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On the representation of generalized axially symmetric potentials in the neighbourhood of an isolated singularity
Author(s) -
Berglez Peter
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310492
Subject(s) - singularity , mathematics , holomorphic function , neighbourhood (mathematics) , axial symmetry , mathematical analysis , pure mathematics , differential operator , operator (biology) , matrix representation , mathematical physics , physics , quantum mechanics , geometry , group (periodic table) , biochemistry , chemistry , repressor , transcription factor , gene
We give explicit representations of generalized axially symmetric potentials using certain differential operators acting on holomorphic functions. This is done for potentials defined in simply connected domains as well as defined in the neighbourhood of an isolated singularity. Further the kernel of an integral operator ‐ the so called Riemann matrix function ‐ is given in an explicit form for an integral representation of the potentials.