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Interpolation Spaces
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Download or read book Interpolation Spaces written by J. Bergh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.
Book Synopsis An Introduction to Sobolev Spaces and Interpolation Spaces by : Luc Tartar
Download or read book An Introduction to Sobolev Spaces and Interpolation Spaces written by Luc Tartar and published by Springer Science & Business Media. This book was released on 2007-05-26 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
Book Synopsis Pick Interpolation and Hilbert Function Spaces by : Jim Agler
Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Society. This book was released on 2023-02-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
Book Synopsis Interpolation and Sampling in Spaces of Analytic Functions by : Kristian Seip
Download or read book Interpolation and Sampling in Spaces of Analytic Functions written by Kristian Seip and published by American Mathematical Soc.. This book was released on 2004 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, an
Book Synopsis Interpolation Functors and Interpolation Spaces by :
Download or read book Interpolation Functors and Interpolation Spaces written by and published by Elsevier. This book was released on 1991-03-18 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the results of that solution, as well as drawing heavily on a classic paper by Aronszajn and Gagliardo, which appeared in 1965 but whose real importance was not realized until a decade later. This includes a systematic use of the language, if not the theory, of categories. In this way the book also opens up many new vistas which still have to be explored. This volume is the first of three planned books. Volume II will deal with the complex method, while Volume III will deal with applications.
Book Synopsis Interpolation Spaces and Allied Topics in Analysis by : M. Cwikel
Download or read book Interpolation Spaces and Allied Topics in Analysis written by M. Cwikel and published by Springer. This book was released on 2006-12-08 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hörmander Spaces, Interpolation, and Elliptic Problems by : Vladimir A. Mikhailets
Download or read book Hörmander Spaces, Interpolation, and Elliptic Problems written by Vladimir A. Mikhailets and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005–2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a reader-friendly style. The complete proofs of theorems are given. This monograph is intended for a wide range of mathematicians whose research interests concern with mathematical analysis and differential equations.
Book Synopsis Interpolation of Operators by : Colin Bennett
Download or read book Interpolation of Operators written by Colin Bennett and published by Academic Press. This book was released on 1988-04-01 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.
Book Synopsis Interpolation Theory by : Alessandra Lunardi
Download or read book Interpolation Theory written by Alessandra Lunardi and published by Springer. This book was released on 2018-05-05 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.
Book Synopsis Smoothed Point Interpolation Methods by : G R Liu
Download or read book Smoothed Point Interpolation Methods written by G R Liu and published by World Scientific. This book was released on 2013-08-16 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Smoothed Point Interpolation Method (S-PIM) has been recently developed. The S-PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations — one of the most important features of the next generation methods. This important book describes the various S-PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the S-PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both S-PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds. The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development. Contents:PreliminariesG SpacesPIM Shape Function CreationStrain Field ConstructionWeak and Weakened Weak FormulationsNode-Based Smoothed Point Interpolation Method (NS-PIM)Edge-Based Smoothed Point Interpolation Method (ES-PIM)Cell-Based Smoothed Point Interpolation Method (CS-PIM)The Cell-Based Smoothed Alpha Radial Point Interpolation Method (CS-αRPIM)Strain-Constructed Point Interpolation Method (SC-PIM)S-PIM for Heat Transfer and Thermoelasticity ProblemsSingular CS-RPIM for Fracture Mechanics ProblemsAdaptive Analysis Using S-PIMsAppendices: Program Codes Library:Description of the SubroutinesA Demonstration Input FileSource Codes of Two ModulesSource Codes of the Common Subroutines Readership: Researchers, practitioners, academics, and graduate students in engineering mechanics, mechanical engineering, aerospace engineering, civil engineering and computational physics. Keywords:Numerical Method;Meshfree Method;Finite Element Method;Point Interpolation Method;G Space;Weakened Weak Form;Applied Mechanics;Adaptive Analysis;Radial Basis Functions;Radial Point Interpolation Method
Book Synopsis Function Spaces, Interpolation Theory and Related Topics by : Michael Cwikel
Download or read book Function Spaces, Interpolation Theory and Related Topics written by Michael Cwikel and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields. Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.
Book Synopsis Weighted Sobolev Spaces by : Alois Kufner
Download or read book Weighted Sobolev Spaces written by Alois Kufner and published by . This book was released on 1985-07-23 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic account of the subject, this book deals with properties and applications of the Sobolev spaces with weights, the weight function being dependent on the distance of a point of the definition domain from the boundary of the domain or from its parts. After an introduction of definitions, examples and auxilliary results, it describes the study of properties of Sobolev spaces with power-type weights, and analogous problems for weights of a more general type. The concluding chapter addresses applications of weighted spaces to the solution of the Dirichlet problem for an elliptic linear differential operator.
Download or read book Sobolev Spaces written by Robert A. Adams and published by Elsevier. This book was released on 2003-06-26 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences. This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike. Self-contained and accessible for readers in other disciplines Written at elementary level making it accessible to graduate students
Book Synopsis Non-Homogeneous Boundary Value Problems and Applications by : Jacques Louis Lions
Download or read book Non-Homogeneous Boundary Value Problems and Applications written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
Book Synopsis The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms by : Gilles Pisier
Download or read book The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1996 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recently developed duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) bounded operators are replaced by completely bounded ones, isomorphisms by complete isomorphisms, and Banach spaces by operator spaces. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into $B(H)$ (with $H$ being Hilbert). In this new category, several operator spaces which are isomorphic (as Banach spaces) to a Hilbert space play an important role. For instance the row and column Hilbert spaces and several other examples appearing naturally in the construction of the Boson or Fermion Fock spaces have been studied extensively. One of the main results of this memoir is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (denoted by $OH$ ) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces. This new concept, called ``the operator Hilbert space'' and denoted by $OH$, is introduced and thoroughly studied in this volume.
Book Synopsis Interpolation Spaces and Related Topics by : Michael Cwikel
Download or read book Interpolation Spaces and Related Topics written by Michael Cwikel and published by . This book was released on 1992 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complex Interpolation between Hilbert, Banach and Operator Spaces by : Gilles Pisier
Download or read book Complex Interpolation between Hilbert, Banach and Operator Spaces written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 2010-10-07 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by a question of Vincent Lafforgue, the author studies the Banach spaces $X$ satisfying the following property: there is a function $\varepsilon\to \Delta_X(\varepsilon)$ tending to zero with $\varepsilon>0$ such that every operator $T\colon \ L_2\to L_2$ with $\T\\le \varepsilon$ that is simultaneously contractive (i.e., of norm $\le 1$) on $L_1$ and on $L_\infty$ must be of norm $\le \Delta_X(\varepsilon)$ on $L_2(X)$. The author shows that $\Delta_X(\varepsilon) \in O(\varepsilon^\alpha)$ for some $\alpha>0$ iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of $\theta$-Hilbertian spaces for some $\theta>0$ (see Corollary 6.7), where $\theta$-Hilbertian is meant in a slightly more general sense than in the author's earlier paper (1979).
