Theory Of Np Spaces
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Theory Of Np Spaces
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Author : Le Hai Khoi
language : en
Publisher: Springer Nature
Release Date : 2023-10-09
Theory Of Np Spaces written by Le Hai Khoi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-09 with Mathematics categories.
This monograph provides a comprehensive study of a typical and novel function space, known as the $\mathcal{N}_p$ spaces. These spaces are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball, and the authors also explore composition operators and weighted composition operators on these spaces. The book covers a significant portion of the recent research on these spaces, making it an invaluable resource for those delving into this rapidly developing area. The authors introduce various weighted spaces, including the classical Hardy space $H^2$, Bergman space $B^2$, and Dirichlet space $\mathcal{D}$. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces $\mathcal{B}^p$ and Bergman-type spaces $A^p$. Additionally, the authors extend their analysis beyond the open unit disk $\mathbb{D}$ and open unit ball $\mathbb{B}$ by presenting families of entire functions in the complex plane $\mathbb{C}$ and in higher dimensions. The Theory of $\mathcal{N}_p$ Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.
Asymptotic Theory Of Finite Dimensional Normed Spaces
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Author : Vitali D. Milman
language : en
Publisher: Springer Science & Business Media
Release Date : 1986
Asymptotic Theory Of Finite Dimensional Normed Spaces written by Vitali D. Milman 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 1986 with Mathematics categories.
Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l^n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other. The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics).
Geometry Of Moduli Spaces And Representation Theory
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Author : Roman Bezrukavnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-15
Geometry Of Moduli Spaces And Representation Theory written by Roman Bezrukavnikov 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 2017-12-15 with Algebraic varieties categories.
This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan–Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry. Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections. The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions.
P Np And Np Completeness
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Author : Oded Goldreich
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-16
P Np And Np Completeness written by Oded Goldreich 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 2010-08-16 with Computers categories.
The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.
Theory Of Function Spaces
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Author : Hans Triebel
language : en
Publisher: Birkhäuser
Release Date : 1983-01-01
Theory Of Function Spaces written by Hans Triebel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Science categories.
The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where ‐∞s∞ and 0p,q≤∞, which include many classical and modern spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rsubn
Introduction To The Theory Of Analytic Spaces
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Author : Raghavan Narasimhan
language : en
Publisher:
Release Date : 1968
Introduction To The Theory Of Analytic Spaces written by Raghavan Narasimhan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Hardy Spaces On Homogeneous Groups
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Author : Gerald B. Folland
language : en
Publisher: Princeton University Press
Release Date : 1982-06-21
Hardy Spaces On Homogeneous Groups written by Gerald B. Folland and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-06-21 with Mathematics categories.
The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.
A Theory Of Cross Spaces
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Author : Robert Schatten
language : en
Publisher:
Release Date : 1950
A Theory Of Cross Spaces written by Robert Schatten and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Mathematics categories.
Probabilistic Normed Spaces
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Author : Bernardo Lafuerza Guillen
language : en
Publisher: World Scientific
Release Date : 2014-08-01
Probabilistic Normed Spaces written by Bernardo Lafuerza Guillen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Mathematics categories.
This book provides a comprehensive foundation in Probabilistic Normed (PN) Spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A N Serstnev in the early 1960s as a response to problems of best approximations in statistics.The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-date and thorough investigation of the properties, uses and applications of PN spaces, based on the standard definition. Topics covered include:The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations. This introduction will therefore have broad relevance across mathematical and statistical research, especially those working in probabilistic functional analysis and probabilistic geometry.
Spaces Worlds And Grammar
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Author : Gilles Fauconnier
language : en
Publisher: University of Chicago Press
Release Date : 1996-12
Spaces Worlds And Grammar written by Gilles Fauconnier and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12 with Language Arts & Disciplines categories.
In the highly influential mental-spaces framework developed by Gilles Fauconnier in the mid-1980s, the mind creates multiple cognitive "spaces" to mediate its understanding of relations and activities in the world, and to engage in creative thought. These twelve original papers extend the mental-spaces framework and demonstrate its utility in solving deep problems in linguistics and discourse theory. Investigating the ties between mental constructs, they analyze a wide range of phenomena, including analogical counterfactuals; the metaphor system for conceptualizing the self; abstract change expressions in Japanese; mood in Spanish; deictic expressions; copular sentences in Japanese; conditional constructions; and reference in American Sign Language. The ground-breaking research presented in this volume will be of interest to linguists and cognitive scientists. The contributors are Claudia Brugman, Gilles Fauconnier, George Lakoff, Yo Matsumoto, Errapel Mejias-Bikandi, Laura A. Michaelis, Gisela Redeker, Jo Rubba, Shigeru Sakahara, Jose Sanders, Eve Sweetser, and Karen van Hoek.