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

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

The Dirichlet area is among the 3 primary Hilbert areas of holomorphic features at the unit disk. It boasts a wealthy and gorgeous thought, but whilst is still a resource of not easy open difficulties and a subject matter of energetic mathematical examine. This booklet is the 1st systematic account of the Dirichlet house, assembling effects formerly in basic terms present in scattered learn articles, and bettering upon the various proofs. subject matters taken care of comprise: the Douglas and Carleson formulation for the Dirichlet necessary, reproducing kernels, boundary behaviour and ability, 0 units and specialty units, multipliers, interpolation, Carleson measures, composition operators, neighborhood Dirichlet areas, shift-invariant subspaces, and cyclicity. certain gains contain a self-contained therapy of potential, together with the strong-type inequality. The e-book could be helpful to researchers in functionality concept, and with over a hundred workouts it's also compatible for self-study by way of graduate students.

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