The Blocking Technique Weighted Mean Operators And Hardy S Inequality

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The Blocking Technique, Weighted Mean Operators and Hardy's Inequality

Karl-Goswin Grosse-Erdmann
The Blocking Technique Weighted Mean Operators and Hardy s Inequality Book PDF

Author : Karl-Goswin Grosse-Erdmann
Publisher : Springer
Page : 122 pages
File Size : 46,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696643

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The Blocking Technique, Weighted Mean Operators and Hardy's Inequality by Karl-Goswin Grosse-Erdmann Pdf

This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis.

Bounded and Compact Integral Operators

David E. Edmunds,V.M Kokilashvili,Alexander Meskhi
Bounded and Compact Integral Operators Book PDF

Author : David E. Edmunds,V.M Kokilashvili,Alexander Meskhi
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 55,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599221

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Bounded and Compact Integral Operators by David E. Edmunds,V.M Kokilashvili,Alexander Meskhi Pdf

The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).

A Dictionary of Inequalities

Peter Bullen
A Dictionary of Inequalities Book PDF

Author : Peter Bullen
Publisher : CRC Press
Page : 298 pages
File Size : 51,5 Mb
Release : 1998-08-21
Category : Mathematics
ISBN : 0582327482

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A Dictionary of Inequalities by Peter Bullen Pdf

The literature on inequalities is vast-in recent years the number of papers as well as the number of journals devoted to the subject have increased dramatically. At best, locating a particular inequality within the literature can be a cumbersome task. A Dictionary of Inequalities ends the dilemma of where to turn to find a result, a related inequality, or the references to the information you need. It provides a concise, alphabetical listing of each inequality-by its common name or its subject-with a short statement of the result, some comments, references to related inequalities, and a list of sources for further information. The author uses only the most elementary of mathematical terminology and does not offer proofs, thus making an interest in inequalities the only prerequisite for using the text. The author focuses on intuitive, physical forms of inequalities rather than their most general versions, and retains the beauty and importance of original versions rather than listing their later, abstract forms. He presents each in its simplest form with other renditions, such as for complex numbers and vectors, as extensions or under different headings. He has kept the book to a more manageable size by omitting inequalities in areas-such as elementary geometric and trigonometric inequalities-rarely used outside their fields. The end result is a current, concise, reference that puts the essential results on inequalities within easy reach. A Dictionary of Inequalities carries the beauty and attraction of the best and most successful dictionaries: on looking up a given item, the reader is likely to be intrigued and led by interest to others.

Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations

Óscar Domínguez,Sergei Tikhonov
Function Spaces of Logarithmic Smoothness Embeddings and Characterizations Book PDF

Author : Óscar Domínguez,Sergei Tikhonov
Publisher : American Mathematical Society
Page : 180 pages
File Size : 42,5 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470455385

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Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations by Óscar Domínguez,Sergei Tikhonov Pdf

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Operators Between Sequence Spaces and Applications

Bruno de Malafosse,Eberhard Malkowsky,Vladimir Rakočević
Operators Between Sequence Spaces and Applications Book PDF

Author : Bruno de Malafosse,Eberhard Malkowsky,Vladimir Rakočević
Publisher : Springer Nature
Page : 379 pages
File Size : 42,8 Mb
Release : 2021-01-19
Category : Mathematics
ISBN : 9789811597428

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Operators Between Sequence Spaces and Applications by Bruno de Malafosse,Eberhard Malkowsky,Vladimir Rakočević Pdf

This book presents modern methods in functional analysis and operator theory along with their applications in recent research. The book also deals with the solvability of infinite systems of linear equations in various sequence spaces. It uses the classical sequence spaces, generalized Cesaro and difference operators to obtain calculations and simplifications of complicated spaces involving these operators. In order to make it self-contained, comprehensive and of interest to a larger mathematical community, the authors have presented necessary concepts with results for advanced research topics. This book is intended for graduate and postgraduate students, teachers and researchers as a basis for further research, advanced lectures and seminars.

Survey on Classical Inequalities

Themistocles RASSIAS
Survey on Classical Inequalities Book PDF

Author : Themistocles RASSIAS
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401143394

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Survey on Classical Inequalities by Themistocles RASSIAS Pdf

Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected] DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: [email protected] Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.

Function Spaces, 1

Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík
Function Spaces 1 Book PDF

Author : Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík
Publisher : Walter de Gruyter
Page : 495 pages
File Size : 43,8 Mb
Release : 2012-12-19
Category : Mathematics
ISBN : 9783110250428

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Function Spaces, 1 by Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík Pdf

This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.

Variational Methods for Crystalline Microstructure - Analysis and Computation

Georg Dolzmann
Variational Methods for Crystalline Microstructure Analysis and Computation Book PDF

Author : Georg Dolzmann
Publisher : Springer
Page : 217 pages
File Size : 54,8 Mb
Release : 2004-10-25
Category : Mathematics
ISBN : 9783540361251

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Variational Methods for Crystalline Microstructure - Analysis and Computation by Georg Dolzmann Pdf

Phase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, often referred to as mathematical materials science, with deep connections to the calculus of variations and the theory of partial differential equations. This volume gives a brief introduction to the essential physical background, in particular for shape memory alloys and a special class of polymers (nematic elastomers). Then the underlying mathematical concepts are presented with a strong emphasis on the importance of quasiconvex hulls of sets for experiments, analytical approaches, and numerical simulations.

Random Times and Enlargements of Filtrations in a Brownian Setting

Roger Mansuy,Marc Yor
Random Times and Enlargements of Filtrations in a Brownian Setting Book PDF

Author : Roger Mansuy,Marc Yor
Publisher : Springer
Page : 158 pages
File Size : 41,9 Mb
Release : 2006-07-25
Category : Mathematics
ISBN : 9783540324164

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Random Times and Enlargements of Filtrations in a Brownian Setting by Roger Mansuy,Marc Yor Pdf

In November 2004, M. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York. These notes follow the contents of that course, covering expansion of filtration formulae; BDG inequalities up to any random time; martingales that vanish on the zero set of Brownian motion; the Azéma-Emery martingales and chaos representation; the filtration of truncated Brownian motion; attempts to characterize the Brownian filtration. The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the progressive kind. It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of Brownian motion.

Combinatorial Stochastic Processes

Jim Pitman
Combinatorial Stochastic Processes Book PDF

Author : Jim Pitman
Publisher : Springer
Page : 260 pages
File Size : 50,5 Mb
Release : 2006-07-21
Category : Mathematics
ISBN : 9783540342663

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Combinatorial Stochastic Processes by Jim Pitman Pdf

The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

Tutorials in Mathematical Biosciences III

Avner Friedman
Tutorials in Mathematical Biosciences III Book PDF

Author : Avner Friedman
Publisher : Springer
Page : 246 pages
File Size : 48,9 Mb
Release : 2005-11-24
Category : Mathematics
ISBN : 9783540324157

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Tutorials in Mathematical Biosciences III by Avner Friedman Pdf

This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.

Abstract Harmonic Analysis of Continuous Wavelet Transforms

Hartmut Führ
Abstract Harmonic Analysis of Continuous Wavelet Transforms Book PDF

Author : Hartmut Führ
Publisher : Springer
Page : 193 pages
File Size : 52,5 Mb
Release : 2005-01-17
Category : Mathematics
ISBN : 9783540315520

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Abstract Harmonic Analysis of Continuous Wavelet Transforms by Hartmut Führ Pdf

This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the volume can also be read as a problem-driven introduction to the Plancherel formula.

Axiom of Choice

Horst Herrlich
Axiom of Choice Book PDF

Author : Horst Herrlich
Publisher : Springer
Page : 198 pages
File Size : 49,7 Mb
Release : 2006-07-21
Category : Mathematics
ISBN : 9783540342687

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Axiom of Choice by Horst Herrlich Pdf

AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. It is shunned by some, used indiscriminately by others. This treatise shows paradigmatically that disasters happen without AC and they happen with AC. Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.

Lattice-Gas Cellular Automata and Lattice Boltzmann Models

Dieter A. Wolf-Gladrow
Lattice Gas Cellular Automata and Lattice Boltzmann Models Book PDF

Author : Dieter A. Wolf-Gladrow
Publisher : Springer
Page : 314 pages
File Size : 40,8 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540465867

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Lattice-Gas Cellular Automata and Lattice Boltzmann Models by Dieter A. Wolf-Gladrow Pdf

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

Calculus of Variations and Geometric Evolution Problems

F. Bethuel,G. Huisken,S. Mueller,K. Steffen
Calculus of Variations and Geometric Evolution Problems Book PDF

Author : F. Bethuel,G. Huisken,S. Mueller,K. Steffen
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 45,6 Mb
Release : 1999-10-19
Category : Mathematics
ISBN : 3540659773

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Calculus of Variations and Geometric Evolution Problems by F. Bethuel,G. Huisken,S. Mueller,K. Steffen Pdf

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.