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A Primer on the Dirichlet Space (Hardcover, New)
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A Primer on the Dirichlet Space (Hardcover, New)
Series: Cambridge Tracts in Mathematics
Expected to ship within 9 - 17 working days
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The Dirichlet space is one of the three fundamental Hilbert spaces
of holomorphic functions on the unit disk. It boasts a rich and
beautiful theory, yet at the same time remains a source of
challenging open problems and a subject of active mathematical
research. This book is the first systematic account of the
Dirichlet space, assembling results previously only found in
scattered research articles, and improving upon many of the proofs.
Topics treated include: the Douglas and Carleson formulas for the
Dirichlet integral, reproducing kernels, boundary behaviour and
capacity, zero sets and uniqueness sets, multipliers,
interpolation, Carleson measures, composition operators, local
Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special
features include a self-contained treatment of capacity, including
the strong-type inequality. The book will be valuable to
researchers in function theory, and with over 100 exercises it is
also suitable for self-study by graduate students.
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