Local L P Brunn Minkowski Inequalities For P
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Local L P Brunn Minkowski Inequalities For P
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Author : Alexander V. Kolesnikov
language : en
Publisher: American Mathematical Society
Release Date : 2022-05-24
Local L P Brunn Minkowski Inequalities For P written by Alexander V. Kolesnikov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-24 with Mathematics categories.
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Geometric Aspects Of Functional Analysis
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Author : Ronen Eldan
language : en
Publisher: Springer Nature
Release Date : 2023-11-01
Geometric Aspects Of Functional Analysis written by Ronen Eldan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-01 with Mathematics categories.
This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.
The Mathematical Legacy Of Victor Lomonosov
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Author : Richard M. Aron
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-08-10
The Mathematical Legacy Of Victor Lomonosov written by Richard M. Aron and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-10 with Mathematics categories.
The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside’s theorem, and the Bishop-Phelps theorem are discussed in detail. This volume is an essential reference to both researchers and graduate students in mathematical analysis.
Convex Geometry
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Author : Shiri Artstein-Avidan
language : en
Publisher: Springer Nature
Release Date : 2023-12-13
Convex Geometry written by Shiri Artstein-Avidan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-13 with Mathematics categories.
This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021. Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn--Minkowski theory currently represents the central part of convex geometry. The Summer School provided an introduction to various aspects of convex geometry: The theory of valuations, including its recent developments concerning valuations on function spaces; geometric and analytic inequalities, including those which come from the Lp Brunn--Minkowski theory; geometric and analytic notions of duality, along with their interplay with mass transportation and concentration phenomena; symmetrizations, which provide one of the main tools to many variational problems (not only in convex geometry). Each of these parts is represented by one of the courses given during the Summer School and corresponds to one of the chapters of the present volume. The initial chapter contains some basic notions in convex geometry, which form a common background for the subsequent chapters. The material of this book is essentially self-contained and, like the Summer School, is addressed to PhD and post-doctoral students and to all researchers approaching convex geometry for the first time.
Harmonic Analysis And Convexity
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Author : Alexander Koldobsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-07-24
Harmonic Analysis And Convexity written by Alexander Koldobsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-24 with Mathematics categories.
In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.
Coefficient Systems On The Bruhat Tits Building And Pro P Iwahori Hecke Modules
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Author : Jan Kohlhaase
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-31
Coefficient Systems On The Bruhat Tits Building And Pro P Iwahori Hecke Modules written by Jan Kohlhaase and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-31 with Mathematics categories.
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Geometric Aspects Of Functional Analysis
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Author : Bo'az Klartag
language : en
Publisher: Springer Nature
Release Date : 2020-06-20
Geometric Aspects Of Functional Analysis written by Bo'az Klartag and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-20 with Mathematics categories.
Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.
Mathematics Going Forward
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Author : Jean-Michel Morel
language : en
Publisher: Springer Nature
Release Date : 2023-06-14
Mathematics Going Forward written by Jean-Michel Morel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-14 with Mathematics categories.
This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.
Intrinsic Approach To Galois Theory Of Q Difference Equations
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Author : Lucia Di Vizio
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-31
Intrinsic Approach To Galois Theory Of Q Difference Equations written by Lucia Di Vizio and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-31 with Mathematics categories.
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Partial Compactification Of Monopoles And Metric Asymptotics
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Author : Chris Kottke
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-10
Partial Compactification Of Monopoles And Metric Asymptotics written by Chris Kottke and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-10 with Mathematics categories.
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