The theory of Hardy spaces has close connections to many branches
of mathematics including Fourier analysis, harmonic analysis,
singular integrals, potential theory and operator theory, and has
found essential applications in robust control engineering. For
each application, the ability to represent elements of these
classes by series or integral formulas is of utmost importance.
This self-contained text provides an introduction to a wide range
of representation theorems and provides a complete description of
the representation theorems with direct proofs for both classes of
Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces
of the upper half plane. With over 300 exercises, many with
accompanying hints, this book is ideal for those studying Advanced
Complex Analysis, Function Theory or Theory of Hardy Spaces.
Advanced undergraduate and graduate students will find the book
easy to follow, with a logical progression from basic theory to
advanced research.
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