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Invariant Potential Theory in the Unit Ball of Cn (London Mathematical Society Lecture Note Series, Series Number 199) (Volume 0)

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Invariant Potential Theory in the Unit Ball of Cn (London Mathematical Society Lecture Note Series, Series Number 199) (Volume 0)

4.85 35,473 ratings · 1,572 reviews
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Overview: This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szego integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.

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ISBN
5621521
Publication date
May 12, 1994
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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After spending years working in the corporate world, Manfred Stoll finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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