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 house is likely one of the 3 primary Hilbert areas of holomorphic features at the unit disk. It boasts a wealthy and lovely concept, but even as is still a resource of difficult open difficulties and a topic of energetic mathematical learn. This booklet is the 1st systematic account of the Dirichlet area, assembling effects formerly in simple terms present in scattered examine articles, and enhancing upon a number of the proofs. issues taken care of comprise: the Douglas and Carleson formulation for the Dirichlet quintessential, reproducing kernels, boundary behaviour and ability, 0 units and distinctiveness units, multipliers, interpolation, Carleson measures, composition operators, neighborhood Dirichlet areas, shift-invariant subspaces, and cyclicity. exact beneficial properties comprise a self-contained remedy of means, together with the strong-type inequality. The e-book should be precious to researchers in functionality thought, and with over a hundred workouts it's also appropriate for self-study through graduate students.

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

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