Analysis on Gaussian Spaces - download pdf or read online

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By Yaozhong Hu

Analysis of features at the finite dimensional Euclidean area with appreciate to the Lebesgue degree is key in arithmetic. The extension to limitless measurement is a brilliant problem a result of loss of Lebesgue degree on countless dimensional house. in its place the preferred degree utilized in limitless dimensional area is the Gaussian degree, which has been unified less than the terminology of "abstract Wiener space".

Out of the massive volume of labor in this subject, this e-book provides a few basic effects plus fresh development. we will current a few effects at the Gaussian area itself corresponding to the Brunn–Minkowski inequality, Small ball estimates, huge tail estimates. the bulk a part of this booklet is dedicated to the research of nonlinear capabilities at the Gaussian area. by-product, Sobolev areas are brought, whereas the well-known Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood–Paley–Stein–Meyer concept are given in details.

This publication comprises a few simple fabric that can not be chanced on somewhere else that the writer believes may be a vital part of the topic. for instance, the e-book comprises a few attention-grabbing and significant inequalities, the Littlewood–Paley–Stein–Meyer thought, and the Hörmander theorem. The e-book additionally contains a few contemporary growth accomplished via the writer and collaborators on density convergence, numerical ideas, neighborhood times.

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Analysis on Gaussian Spaces by Yaozhong Hu

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