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  3. A Primer on the Dirichlet Space
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  • Publisher:
    Cambridge University Press
    Publication date:
    05 January 2014
    16 January 2014
    ISBN:
    9781107239425
    9781107047525
    DOI:
    https://doi.org/10.1017/CBO9781107239425
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.47kg, 226 Pages
    Dimensions:
    Weight & Pages:
    • Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Real and Complex Analysis
    Series:
    Cambridge Tracts in Mathematics (203)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Real and Complex Analysis
    Series:
    Cambridge Tracts in Mathematics (203)
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    Book description

    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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