In the recent years, the interplay between the methods of functional analysis
and complex analysis has led to some remarkable results in a wide variety of topics.
It turned out that the structure of spaces of holomorphic functions is fundamen-
tally linked to certain invariants initially defined on abstract Fr´ echet spaces as well
as the developments in pluripotential theory. The developments in the theory of
the projective limit functor and its interaction with the questions related to the
solvability of linear partial differential operators by operators in
or global
solvability in A(Ω), has been another area where a rich variety of new results were
obtained. With these new tools, extension properties of functions defined on real
analytic varieties and real analytic composition operators can be treated and the
surprising result on the non-existence of bases in spaces of real analytic functions
can be proved.
The aim of this volume is to document some of the original contributions to this
topic presented at a conference held in Sabancı University in
Istanbul, September
17-21, 2007. It also contains some surveys to give an overview of the state of the
art and to initiate further research in the interplay between functional and complex
analysis. The third day of the meeting was reserved to celebrate the 70th birthday
of Vyacheslav Zakharyuta, who is certainly one of the pioneers in this field. The
efforts of the local organizing committee, Bedia Kolatar, Buket Can Bahadır and
Murat Yurdakul, as well as the staff of Sabancı University, contributed to the
success of our meeting.
Finally, we would like to thank to all the participants to the conference.
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