{"product_id":"an-introduction-to-infinite-dimensional-analysis-9783540290209","title":"An Introduction to Infinite-Dimensional Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eBased on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"This is an extended version of the author’s ‘An introduction to infinite-dimensional analysis’ published by Scuola Normale Superiore, Pisa … . A well written textbook (even an introductory research monograph), suitable for teaching a graduate course.\" (Neils Jacob, Zentralblatt MATH, Vol. 1109 (11), 2007)\u003c\/p\u003e \u003cp\u003e\"The present volume collects together … the notes of the course on infinite-dimensional analysis held by the author at the Scuola Normale Superiore of Pisa in recent years. The book is intended for people who have some knowledge of functional analysis … . It provides an extremely useful tool for those scholars who are interested in learning some basics about Gaussian measures in Hilbert spaces, Brownian motion, Markov transition semigroups … . The book is well written and all arguments are clearly and rigorously presented.\" (Sandra Cerrai, Mathematical Reviews, Issue 2009 a)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGaussian measures in Hilbert spaces.- The Cameron–Martin formula.- Brownian motion.- Stochastic perturbations of a dynamical system.- Invariant measures for Markov semigroups.- Weak convergence of measures.- Existence and uniqueness of invariant measures.- Examples of Markov semigroups.- L2 spaces with respect to a Gaussian measure.- Sobolev spaces for a Gaussian measure.- Gradient systems.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":53196963742039,"sku":"9783540290209","price":35.99,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/an-introduction-to-infinite-dimensional-analysis-9783540290209","provider":"Book Curl","version":"1.0","type":"link"}