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# đź“™ A Primer on the Dirichlet Space by Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford â€” free epub

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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.

## About book:

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- Series:
**Cambridge Tracts in Mathematics 203** - Author:
**Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford** - Year:
**2014** - Publisher:
**Cambridge University Press** - Language:
**English** - ISBN:
**1107047528,9781107047525**

- File size:
**1 248 724** - Format:
**pdf**

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Contents: I General Dirichlet forms. . . . . . . . 1 Closed forms ............. 2 Sub-Markovian symmetric operators 3 Dirichlet forms and Dirichlet operators 4 The carre du champ operator 5 Locality................. 6 FUnctional calculus . ...

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quic...

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quic...

The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, SchrĂ¶dinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-...

The concise yet authoritative presentation of key techniques for basic mixtures experimentsInspired by the author's bestselling advanced book on the topic, A Primer on Experiments with Mixtures provides an introductory presentation of the key principles b...

The concise yet authoritative presentation of key techniques for basic mixtures experimentsInspired by the author's bestselling advanced book on the topic, A Primer on Experiments with Mixtures provides an introductory presentation of the key principles b...

This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale fo...

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature su...

The first of two planned volumes on Banach-space isometries, this text characterizes isometries and describes them in classical function spaces. Fleming (mathematics, Central Michigan U.) and Jamison (mathematical sciences, U. of Memphis) give historicall...