Q Analysis On Euclidean Spaces

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Nonlinear Analysis On Manifolds Sobolev Spaces And Inequalities
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Author : Emmanuel Hebey
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-10-27
Nonlinear Analysis On Manifolds Sobolev Spaces And Inequalities written by Emmanuel Hebey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-27 with Mathematics categories.
This volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. ``Several surprising phenomena appear when studying Sobolev spaces on manifolds,'' according to the author. ``Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role.'' The volume is organized into nine chapters. Chapter 1 offers a brief introduction to differential and Riemannian geometry. Chapter 2 deals with the general theory of Sobolev spaces for compact manifolds. Chapter 3 presents the general theory of Sobolev spaces for complete, noncompact manifolds. Best constants problems for compact manifolds are discussed in Chapters 4 and 5. Chapter 6 presents special types of Sobolev inequalities under constraints. Best constants problems for complete noncompact manifolds are discussed in Chapter 7. Chapter 8 deals with Euclidean-type Sobolev inequalities. And Chapter 9 discusses the influence of symmetries on Sobolev embeddings. An appendix offers brief notes on the case of manifolds with boundaries. This topic is a field undergoing great development at this time. However, several important questions remain open. So a substantial part of the book is devoted to the concept of best constants, which appeared to be crucial for solving limiting cases of some classes of PDEs. The volume is highly self-contained. No familiarity is assumed with differentiable manifolds and Riemannian geometry, making the book accessible to a broad audience of readers, including graduate students and researchers.
Stochastic Analysis On Infinite Dimensional Spaces
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Author : H Kunita
language : en
Publisher: CRC Press
Release Date : 1994-08-22
Stochastic Analysis On Infinite Dimensional Spaces written by H Kunita and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-08-22 with Mathematics categories.
The book discusses the following topics in stochastic analysis: 1. Stochastic analysis related to Lie groups: stochastic analysis of loop spaces and infinite dimensional manifolds has been developed rapidly after the fundamental works of Gross and Malliavin. (Lectures by Driver, Gross, Mitoma, and Sengupta.)
A Course In Mathematical Analysis Volume 2 Metric And Topological Spaces Functions Of A Vector Variable
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Author : D. J. H. Garling
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-23
A Course In Mathematical Analysis Volume 2 Metric And Topological Spaces Functions Of A Vector Variable written by D. J. H. Garling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-23 with Mathematics categories.
The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.
Henstock Kurzweil Integration On Euclidean Spaces
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Author : Tuo Yeong Lee
language : en
Publisher: World Scientific
Release Date : 2011
Henstock Kurzweil Integration On Euclidean Spaces written by Tuo Yeong Lee and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The Henstock?Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock?Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.
Q Series Their Development And Application In Analysis Number Theory Combinatorics Physics And Computer Algebra
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Author : George E. Andrews
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Q Series Their Development And Application In Analysis Number Theory Combinatorics Physics And Computer Algebra written by George E. Andrews and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Integrates developments and related applications in $q$-series with a historical development of the field. This book develops important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory.
Introduction To Abstract Analysis
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Author : Marvin E. Goldstein
language : en
Publisher: Courier Corporation
Release Date : 2015-02-18
Introduction To Abstract Analysis written by Marvin E. Goldstein and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-18 with Mathematics categories.
Concise text prepares readers to pursue abstract analysis in the literature of pure mathematics. Detailed, easy-to-follow proofs and examples illustrate topics including real numbers, vector and metric spaces, infinite series, and other concepts. 1969 edition.
Stochastic Analysis Filtering And Stochastic Optimization
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Author : George Yin
language : en
Publisher: Springer Nature
Release Date : 2022-04-22
Stochastic Analysis Filtering And Stochastic Optimization written by George Yin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-22 with Mathematics categories.
This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.
Wavelet Analysis
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Author : Sabrine Arfaoui
language : en
Publisher: CRC Press
Release Date : 2021-04-20
Wavelet Analysis written by Sabrine Arfaoui and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-20 with Mathematics categories.
Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained introduction to the ideas underpinning wavelet theory and its diverse applications. This book is suitable for master’s or PhD students, senior researchers, or scientists working in industrial settings, where wavelets are used to model real-world phenomena and data needs (such as finance, medicine, engineering, transport, images, signals, etc.). Features: Offers a self-contained discussion of wavelet theory Suitable for a wide audience of post-graduate students, researchers, practitioners, and theorists Provides researchers with detailed proofs Provides guides for readers to help them understand and practice wavelet analysis in different areas
Fourier Analysis In Convex Geometry
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Author : Alexander Koldobsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-11-12
Fourier Analysis In Convex Geometry written by Alexander Koldobsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-12 with Mathematics categories.
The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the -dimensional volume of hyperplane sections of the -dimensional unit cube (it is for each ). Another is the Busemann-Petty problem: if and are two convex origin-symmetric -dimensional bodies and the -dimensional volume of each central hyperplane section of is less than the -dimensional volume of the corresponding section of , is it true that the -dimensional volume of is less than the volume of ? (The answer is positive for and negative for .) The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.
New Trends In Applied Harmonic Analysis Volume 2
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Author : Akram Aldroubi
language : en
Publisher: Springer Nature
Release Date : 2019-11-26
New Trends In Applied Harmonic Analysis Volume 2 written by Akram Aldroubi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with Mathematics categories.
This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.