By Yaozhong Hu
Analysis of services at the finite dimensional Euclidean house with appreciate to the Lebesgue degree is key in arithmetic. The extension to countless size is a brilliant problem a result of loss of Lebesgue degree on limitless dimensional house. in its place the most well-liked degree utilized in countless dimensional area is the Gaussian degree, which has been unified lower than the terminology of "abstract Wiener space".
Out of the massive quantity of labor in this subject, this ebook provides a few primary effects plus fresh development. we will current a few effects at the Gaussian area itself similar to the Brunn–Minkowski inequality, Small ball estimates, huge tail estimates. the bulk a part of this publication is dedicated to the research of nonlinear services at the Gaussian area. by-product, Sobolev areas are brought, whereas the recognized Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood–Paley–Stein–Meyer concept are given in details.
This ebook contains a few uncomplicated fabric that can not be came upon in different places that the writer believes will be a vital part of the topic. for instance, the ebook contains a few fascinating and significant inequalities, the Littlewood–Paley–Stein–Meyer concept, and the Hörmander theorem. The booklet additionally contains a few fresh growth completed by means of the writer and collaborators on density convergence, numerical ideas, neighborhood times.
Read Online or Download Analysis on Gaussian Spaces PDF
Similar functional analysis books
To summarize in brief, this publication is dedicated to an exposition of the rules of pseudo differential equations thought in non-smooth domain names. the weather of this kind of thought exist already within the literature and will be present in such papers and monographs as [90,95,96,109,115,131,132,134,135,136,146, 163,165,169,170,182,184,214-218].
This ebook presents an intensive and self-contained examine of interdependence and complexity in settings of useful research, harmonic research and stochastic research. It makes a speciality of 'dimension' as a uncomplicated counter of levels of freedom, resulting in special kinfolk among combinatorial measurements and numerous indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck.
Such a lot latest books on evolution equations have a tendency both to hide a selected type of equations in an excessive amount of intensity for novices or specialize in a truly particular examine path. hence, the sphere should be daunting for beginners to the sector who want entry to initial fabric and behind-the-scenes aspect.
Reprinted because it initially seemed within the 1990s, this paintings is as an inexpensive text that might be of curiosity to more than a few researchers in geometric research and mathematical physics. The book covers a variety of techniques basic to the research and purposes of the spin-c Dirac operator, employing the warmth kernels concept of Berline, Getzlet, and Vergne.
Additional info for Analysis on Gaussian Spaces
Analysis on Gaussian Spaces by Yaozhong Hu