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Author : Mark Aleksandrovich Krasnoselʹskiĭ
Publisher : Unknown
Page : 224 pages
File Size : 47,6 Mb
Release : 1960
Category : Convex domains
ISBN : MINN:31951D03778752X
Author : Mark Aleksandrovich Krasnoselʹskiĭ,I︠A︡kov Bronislavovich Rutit︠s︡kiĭ
Publisher : Unknown
Page : 262 pages
File Size : 49,9 Mb
Release : 1962
Category : Convex domains
ISBN : LCCN:sa63001074
Author : Peter Kosmol,Dieter Müller-Wichards
Publisher : Walter de Gruyter
Page : 405 pages
File Size : 52,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110250206
This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus
Author : J. Musielak
Publisher : Springer
Page : 227 pages
File Size : 46,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540386926
Author : Petteri Harjulehto,Peter Hästö
Publisher : Springer
Page : 169 pages
File Size : 47,5 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9783030151003
This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
Author : M.M. Rao,Z.D. Ren
Publisher : CRC Press
Page : 486 pages
File Size : 41,5 Mb
Release : 2002-02-08
Category : Mathematics
ISBN : 9780203910863
Presents previously unpublished material on the fundumental pronciples and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes. Provides practical applications in statistics and probability.
Author : G. G. Lorentz
Publisher : Unknown
Page : 16 pages
File Size : 40,9 Mb
Release : 1959
Category : Function spaces
ISBN : UOM:39015095257567
Author : M.M. Rao,Z.D. Ren
Publisher : CRC Press
Page : 496 pages
File Size : 52,6 Mb
Release : 2002-02-08
Category : Mathematics
ISBN : 0203910869
Presents previously unpublished material on the fundumental pronciples and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes. Provides practical applications in statistics and probability.
Author : M.M. Rao,Z.D. Ren
Publisher : CRC Press
Page : 472 pages
File Size : 42,5 Mb
Release : 1991-03-14
Category : Mathematics
ISBN : 0824784782
A reference/text for mathematicians or students involved in analysis, differential equations, probability theory, and the study of integral operators where only Lebesgue spaces were used in the past. Updates and extends the pioneering work by Krasnosel'skii and Rutickii in their 1958 treatise on Orl
Author : Constantin P. Niculescu,Lars-Erik Persson
Publisher : Springer
Page : 415 pages
File Size : 40,7 Mb
Release : 2018-06-08
Category : Mathematics
ISBN : 9783319783376
Thorough introduction to an important area of mathematics Contains recent results Includes many exercises
Author : Henryk Hudzik,Leszek Skrzypcazk
Publisher : CRC Press
Page : 538 pages
File Size : 49,7 Mb
Release : 2000-07-18
Category : Mathematics
ISBN : 0824704193
This volume compiles research results from the fifth Function Spaces International Conference, held in Poznan, Poland. It presents key advances, modern applications and analyses of function spaces and contains two special sections recognizing the contributions and influence of Wladyslaw Orlicz and Genadil Lozanowskii.
Author : Vakhtang Kokilashvili,Miroslav Krbec
Publisher : World Scientific
Page : 248 pages
File Size : 53,6 Mb
Release : 1991-12-31
Category : Mathematics
ISBN : 9789814506281
This book is intended as a survey of latest results on weighted inequalities in Lorentz, Orlicz spaces and Zygmund classes. During the last few years they have become one of the mostdeveloped offshoots of the theory of the harmonic analysis operators. Up to now there has been no monograph devoted to these questions, the results are mostly scattered in various journals and a part of the book consists of results not published anywhere else. Many of theorems presented have only previously been published in Russian. Contents:Integral Operators in Nonweighted Orlicz ClassesMaximal Functions and Potentials in Weighted Orlicz ClassesSingular Integrals in Weighted Orlicz ClassesIntegral Operators in Weighted Zygmund ClassesFractional Maximal Function in Weighted Lorentz SpacesPotentials and Riesz Transforms in Weighted Lorentz Spaces Readership: Mathematicians, graduate students and researchers in real and complex analysis. keywords:Orlicz Space;Lorentz Space;Zygmund Space;Weighted Space;Ap Weight;Maximal Operator;Riesz Potential;Hilbert Transform;Singular Integral;Weighted Inequalities “The authors, together with various collaborators, have made important contributions to the field over the last decade … The exposition is clear with detailed proofs of all statements and the monograph will certainly be a good supplement to survey articles and books on the weighted inequalities.” Mathematical Reviews
Author : Vakhtang Mikha?lovich Kokilashvili,Miroslav Krbec
Publisher : World Scientific
Page : 250 pages
File Size : 51,7 Mb
Release : 1991
Category : Mathematics
ISBN : 9810206127
This book is intended as a survey of latest results on weighted inequalities in Lorentz, Orlicz spaces and Zygmund classes. During the last few years they have become one of the mostdeveloped offshoots of the theory of the harmonic analysis operators. Up to now there has been no monograph devoted to these questions, the results are mostly scattered in various journals and a part of the book consists of results not published anywhere else. Many of theorems presented have only previously been published in Russian.
Author : Krzysztof Jarov
Publisher : CRC Press
Page : 450 pages
File Size : 49,8 Mb
Release : 1991-12-23
Category : Mathematics
ISBN : 0824786122
This book is based on the conference on Function Spaces held at Southern Illinois University at Edwardsville, in April, 1990. It is designed to cover a wide range of topics, including spaces of analytic functions, isometries of function spaces, geometry of Banach spaces, and Banach algebras.
Author : Iwona Chlebicka,Piotr Gwiazda,Agnieszka Świerczewska-Gwiazda,Aneta Wróblewska-Kamińska
Publisher : Springer Nature
Page : 389 pages
File Size : 45,5 Mb
Release : 2021-11-01
Category : Mathematics
ISBN : 9783030888565
This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth. The common property of the many different kinds of equations considered is that the growth conditions of the highest order operators lead to a formulation of the equations in Musielak–Orlicz spaces. This high level of generality, understood as full anisotropy and inhomogeneity, requires new proof concepts and a generalization of the formalism, calling for an extended functional analytic framework. This theory is established in the first part of the book, which serves as an introduction to the subject, but is also an important ingredient of the whole story. The second part uses these theoretical tools for various types of PDEs, including abstract and parabolic equations but also PDEs arising from fluid and solid mechanics. For connoisseurs, there is a short chapter on homogenization of elliptic PDEs. The book will be of interest to researchers working in PDEs and in functional analysis.
