Some Connections Between Isoperimetric And Sobolev Type Inequalities
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Some Connections Between Isoperimetric And Sobolev Type Inequalities
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Author : Serguei Germanovich Bobkov
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Some Connections Between Isoperimetric And Sobolev Type Inequalities written by Serguei Germanovich Bobkov 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 1997 with Art categories.
For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.
Concentration Functional Inequalities And Isoperimetry
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Author : Christian Houdré
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Concentration Functional Inequalities And Isoperimetry written by Christian Houdré 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 2011 with Mathematics categories.
The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, with recent new applications in random matrices and information theory. This will appeal to graduate students and researchers interested in the interplay between analysis, probability, and geometry.
Relations Related To Betweenness Their Structure And Automorphisms
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Author : Samson Adepoju Adeleke
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Relations Related To Betweenness Their Structure And Automorphisms written by Samson Adepoju Adeleke 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 1998 with Mathematics categories.
This volume is about tree-like structures, namely semilinear ordering, general betweenness relations, C-relations and D-relations. It contains a systematic study of betweenness and introduces C- and D- relations to describe the behaviour of points at infinity (leaves or ends or directions of trees). The focus is on structure theorems and on automorphism groups, with applications to the theory of infinite permutation groups.
Hodge Theory In The Sobolev Topology For The De Rham Complex
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Author : Luigi Fontana
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Hodge Theory In The Sobolev Topology For The De Rham Complex written by Luigi Fontana 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 1998 with Mathematics categories.
In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds.
Geometry Of Isotropic Convex Bodies
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Author : Silouanos Brazitikos
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-24
Geometry Of Isotropic Convex Bodies written by Silouanos Brazitikos 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 2014-04-24 with Mathematics categories.
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
The Study Of Minimax Inequalities And Applications To Economies And Variational Inequalities
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Author : George Xian-Zhi Yuan
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
The Study Of Minimax Inequalities And Applications To Economies And Variational Inequalities written by George Xian-Zhi Yuan 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 1998 with Mathematics categories.
This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.
A Continuum Limit Of The Toda Lattice
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Author : Percy Deift
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
A Continuum Limit Of The Toda Lattice written by Percy Deift 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 1998 with Mathematics categories.
In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.
Around The Research Of Vladimir Maz Ya I
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Author : Ari Laptev
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-02
Around The Research Of Vladimir Maz Ya I written by Ari Laptev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-02 with Mathematics categories.
The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz'ya inequalities, Maz'ya's isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.
Approaching The Kannan Lov Sz Simonovits And Variance Conjectures
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Author : David Alonso-Gutiérrez
language : en
Publisher: Springer
Release Date : 2015-01-07
Approaching The Kannan Lov Sz Simonovits And Variance Conjectures written by David Alonso-Gutiérrez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-07 with Mathematics categories.
Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovász-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the treated topics. Offering a presentation suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, giving the interested reader rapid access to the core of these conjectures. In addition, four recent and important results in this theory are presented in a compelling way. The first two are theorems due to Eldan-Klartag and Ball-Nguyen, relating the variance and the KLS conjectures, respectively, to the hyperplane conjecture. Next, the main ideas needed prove the best known estimate for the thin-shell width given by Guédon-Milman and an approach to Eldan's work on the connection between the thin-shell width and the KLS conjecture are detailed.
Basic Almost Poised Hypergeometric Series
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Author : Wenchang Chu
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Basic Almost Poised Hypergeometric Series written by Wenchang Chu 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 1998 with Mathematics categories.
Presents a systematic treatment for the evaluation of basic almost poised series. Some 200 identities are covered, among which most are believed to be new. Their connections with the q-Clausen formulae as well as Rogers-Ramanujan identities are sketched. No index. Annotation copyrighted by Book News, Inc., Portland, OR