Complex Analysis On Infinite Dimensional Spaces (springer Monographs In Mathematics)
by Sean Dineen /
1999 / English / DjVu
3.6 MB Download
This book considers basic questions connected with, and arising
from, the locally convex space structures that may be placed on the
space of holomorphic functions over a locally convex space. The
first three chapters introduce the basic properties of polynomials
and holomorphic functions over locally convex spaces. These are
followed by two chapters concentrating on relationships between the
compact open topology, the ported or Nachbin topology and the
topology generated by the countable open covers. The concluding
chapter examines the interplay between the various concepts
introduced earlier as being intrinsic to infinite dimensional
holomorphy. The comprehensive notes, historical background,
exercises, appendix and bibliography make this book an invaluable
reference whilst the presentation and synthesis of ideas from
different areas will appeal to mathematicians from many different
backgrounds.
This book considers basic questions connected with, and arising
from, the locally convex space structures that may be placed on the
space of holomorphic functions over a locally convex space. The
first three chapters introduce the basic properties of polynomials
and holomorphic functions over locally convex spaces. These are
followed by two chapters concentrating on relationships between the
compact open topology, the ported or Nachbin topology and the
topology generated by the countable open covers. The concluding
chapter examines the interplay between the various concepts
introduced earlier as being intrinsic to infinite dimensional
holomorphy. The comprehensive notes, historical background,
exercises, appendix and bibliography make this book an invaluable
reference whilst the presentation and synthesis of ideas from
different areas will appeal to mathematicians from many different
backgrounds.
