Tools For Infinite Dimensional Analysis
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Author | : Jeremy J. Becnel |
Publisher | : CRC Press |
Total Pages | : 289 |
Release | : 2020-12-28 |
Genre | : Mathematics |
ISBN | : 1000328260 |
Download Tools for Infinite Dimensional Analysis Book in PDF, Epub and Kindle
Over the past six decades, several extremely important fields in mathematics have been developed. Among these are Itô calculus, Gaussian measures on Banach spaces, Malliavan calculus, and white noise distribution theory. These subjects have many applications, ranging from finance and economics to physics and biology. Unfortunately, the background information required to conduct research in these subjects presents a tremendous roadblock. The background material primarily stems from an abstract subject known as infinite dimensional topological vector spaces. While this information forms the backdrop for these subjects, the books and papers written about topological vector spaces were never truly written for researchers studying infinite dimensional analysis. Thus, the literature for topological vector spaces is dense and difficult to digest, much of it being written prior to the 1960s. Tools for Infinite Dimensional Analysis aims to address these problems by providing an introduction to the background material for infinite dimensional analysis that is friendly in style and accessible to graduate students and researchers studying the above-mentioned subjects. It will save current and future researchers countless hours and promote research in these areas by removing an obstacle in the path to beginning study in areas of infinite dimensional analysis. Features Focused approach to the subject matter Suitable for graduate students as well as researchers Detailed proofs of primary results
Author | : Charalambos D. Aliprantis |
Publisher | : |
Total Pages | : 624 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662030059 |
Download Infinite Dimensional Analysis Book in PDF, Epub and Kindle
Author | : Giuseppe Da Prato |
Publisher | : Springer Science & Business Media |
Total Pages | : 217 |
Release | : 2006-08-25 |
Genre | : Mathematics |
ISBN | : 3540290214 |
Download An Introduction to Infinite-Dimensional Analysis Book in PDF, Epub and Kindle
Based 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.
Author | : Charalambos D. Aliprantis |
Publisher | : |
Total Pages | : 604 |
Release | : 1994 |
Genre | : Economics |
ISBN | : 9783662030066 |
Download Infinite Dimensional Analysis Book in PDF, Epub and Kindle
This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast amount of material that spans several traditional fields in mathematics. Much of the mate rial appears only in esoteric research monographs that are designed for specialists, not for the sort of generalist that our students need be. We hope that in a small way this text will make the material here accessible to a much broader audience. While our motivation is to present and orga nize the analytical foundations underlying modern economics and finance, this is a book of mathematics, not of economics. We mention applications to economics but present very few of them. They are there to convince economists that the material has so me relevance and to let mathematicians know that there are areas of application for these results. We feel that this text could be used for a course in analysis that would benefit math ematicians, engineers, and scientists. Most of the material we present is available elsewhere, but is scattered throughout a variety of sources and occasionally buried in obscurity. Some of our results are original (or more likely, independent rediscoveries). We have included some material that we cannot honestly say is neces sary to understand modern economic theory, but may yet prove useful in future research.
Author | : James K. Peterson |
Publisher | : CRC Press |
Total Pages | : 469 |
Release | : 2020-07-19 |
Genre | : Mathematics |
ISBN | : 1351679309 |
Download Basic Analysis III Book in PDF, Epub and Kindle
Basic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist. Feature: Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasizes learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Author | : Nobuaki Obata |
Publisher | : |
Total Pages | : 232 |
Release | : 2001 |
Genre | : |
ISBN | : |
Download Infinite Dimensional Analysis and Quantum Probability Theory Book in PDF, Epub and Kindle
Author | : Palle Jorgensen |
Publisher | : World Scientific |
Total Pages | : 253 |
Release | : 2021-01-15 |
Genre | : Mathematics |
ISBN | : 9811225796 |
Download Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory Book in PDF, Epub and Kindle
The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.
Author | : L. Accardi |
Publisher | : World Scientific |
Total Pages | : 390 |
Release | : 1993 |
Genre | : Science |
ISBN | : 9789810211400 |
Download Quantum Probability and Related Topics Book in PDF, Epub and Kindle
Quantum Probability and Related Topics is a series of volumes based on material discussed at the various QP conferences. It aims to provide an update on the rapidly growing field of classical probability, quantum physics and functional analysis.
Author | : Michael I. Gil' |
Publisher | : Springer Science & Business Media |
Total Pages | : 386 |
Release | : 1998-09-30 |
Genre | : Mathematics |
ISBN | : 9780792382218 |
Download Stability of Finite and Infinite Dimensional Systems Book in PDF, Epub and Kindle
The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
Author | : Taku Matsui |
Publisher | : World Scientific |
Total Pages | : 447 |
Release | : 2003-01-16 |
Genre | : Science |
ISBN | : 9814486507 |
Download Non-commutativity, Infinite-dimensionality And Probability At The Crossroads, Procs Of The Rims Workshop On Infinite-dimensional Analysis And Quantum Probability Book in PDF, Epub and Kindle
Infinite-dimensional analysis and quantum probability have undergone significant developments in the last few years and created many applications. This volume includes four expository articles on recent developments in quantum field theory, quantum stochastic differential equations, free probability and quantum white noise calculus, which are targeted also for graduate study. The fourteen research papers deal with most of the current topics, and their interconnections reflect a vivid development in interacting Fock space, infinite-dimensional groups, stochastic independence, non-commutative central limit theorems, stochastic geometry, and so on.