4. Extension of separately holomorphic functions with
singularities
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Polish supervisor:
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Marek Jarnicki
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Cooperating partners:
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Peter Pflug (Carl von Ossietzky Universitat, Oldenburg)
Raimar Wulkenhaar (Universitat Munster)
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The problems related to extension of separately
holomorphic/meromorphic functions (with or without singularities)
have been fundamental for complex analysis since its origin at the
end of the 19th century. Initially, the extension problems
concerned separately holomorphic or meromorphic functions defined
on Cartesian products - F.Hartogs (1906), M.Hukuhara (1930),
W.Rothstein (1950), I.Shimoda (1957), T.Terada (1967-1972). Next,
in 1969, J.Siciak begun studying functions defined on more general
objects - crosses and N-fold crosses. The research has been
continued by, for instance, Nguyen Thanh Van, V.P. Zahariuta, and
A.Zeriahi (1991-2001). Finally, in 1987, E.M.Chirka and
A.Sadullaev started to study extension problems with
singularities. This type of extension problem has been very
extensively studied in recent years - O.Oektem (1989-1990),
J.Siciak (2001), M.Jarnicki-P.Pflug (2001-2010). The aim of the
proposed topic is to find a counterpart of the extension theory
with singularities for a new category of so called (N,k)-crosses.
The problem is difficult and therefore some partial results would
be sufficient for a good PhD thesis.
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