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.
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 Mathematics 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.
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.
Composition Operators On Spaces Of Analytic Functions
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Author : Carl C. Cowen, Jr.
language : en
Publisher: CRC Press
Release Date : 1995-04-27
Composition Operators On Spaces Of Analytic Functions written by Carl C. Cowen, Jr. and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-27 with Mathematics categories.
The study of composition operators lies at the interface of analytic function theory and operator theory. Composition Operators on Spaces of Analytic Functions synthesizes the achievements of the past 25 years and brings into focus the broad outlines of the developing theory. It provides a comprehensive introduction to the linear operators of composition with a fixed function acting on a space of analytic functions. This new book both highlights the unifying ideas behind the major theorems and contrasts the differences between results for related spaces. Nine chapters introduce the main analytic techniques needed, Carleson measure and other integral estimates, linear fractional models, and kernel function techniques, and demonstrate their application to problems of boundedness, compactness, spectra, normality, and so on, of composition operators. Intended as a graduate-level textbook, the prerequisites are minimal. Numerous exercises illustrate and extend the theory. For students and non-students alike, the exercises are an integral part of the book. By including the theory for both one and several variables, historical notes, and a comprehensive bibliography, the book leaves the reader well grounded for future research on composition operators and related areas in operator or function theory.
The Space Of Mathematics
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Author : Javier Echeverria
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-25
The Space Of Mathematics written by Javier Echeverria and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-25 with Mathematics categories.
No detailed description available for "The Space of Mathematics".
Computational Complexity
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Author : Sanjeev Arora
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-20
Computational Complexity written by Sanjeev Arora 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 2009-04-20 with Computers categories.
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Composition Operators And Classical Function Theory
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Author : Joel H. Shapiro
language : en
Publisher:
Release Date : 1993
Composition Operators And Classical Function Theory written by Joel H. Shapiro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The study of composition operators forges links between fundamental properties of linear operators and beautiful results from the classical theory of analytic functions. This book provides a self-contained introduction to both the subject and its function-theoretic underpinnings. The development is geometrically motivated, and accessible to anyone who has studied basic graduate-level real and complex analysis. The work explores how operator-theoretic issues such as boundedness, compactness, and cyclicity evolve - in the setting of composition operators on the Hilbert space H2 into questions about subordination, value distribution, angular derivatives, iteration, and functional equations. Each of these classical topics is developed fully, and particular attention is paid to their common geometric heritage as descendants of the Schwarz Lemma.
Operator Theory In Function Spaces
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Author : Kehe Zhu
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Operator Theory In Function Spaces written by Kehe Zhu 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 2007 with Mathematics categories.
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Computation And Automata
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Author : Arto Salomaa
language : en
Publisher: Cambridge University Press
Release Date : 1985-05-23
Computation And Automata written by Arto Salomaa 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 1985-05-23 with Computers categories.
In this book, which was originally published in 1985, Arto Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography.