A Primer on the Dirichlet Space (Cambridge Tracts in by Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford

By Omar El-Fallah,Karim Kellay,Javad Mashreghi,Thomas Ransford

The Dirichlet house is among the 3 basic Hilbert areas of holomorphic services at the unit disk. It boasts a wealthy and lovely idea, but even as continues to be a resource of hard open difficulties and an issue of energetic mathematical study. This ebook is the 1st systematic account of the Dirichlet area, assembling effects formerly in simple terms present in scattered learn articles, and bettering upon the various proofs. issues handled contain: the Douglas and Carleson formulation for the Dirichlet crucial, reproducing kernels, boundary behaviour and capability, 0 units and specialty units, multipliers, interpolation, Carleson measures, composition operators, neighborhood Dirichlet areas, shift-invariant subspaces, and cyclicity. distinctive positive aspects comprise a self-contained therapy of ability, together with the strong-type inequality. The booklet may be beneficial to researchers in functionality conception, and with over a hundred routines it's also appropriate for self-study by means of graduate students.

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