Author: Josef KralPublisher: Springer
ISBN: 3540382887
Category : Mathematics
Languages : en
Pages : 175
Book Description
Integral Operators in Potential Theory
Author: Josef KralPublisher: Springer
ISBN: 3540382887
Category : Mathematics
Languages : en
Pages : 175
Book Description
Cyclic Neofields and Combinatorial Designs
Author: Derbiau Frank HsuPublisher:
ISBN: 9780387102276
Category : Algebraic fields
Languages : en
Pages : 170
Book Description
Integral operators in potential theory
Author: Josef KrálBounded and Compact Integral Operators
Author: David E. EdmundsPublisher: Springer Science & Business Media
ISBN: 940159922X
Category : Mathematics
Languages : en
Pages : 655
Book Description
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).
Integral Operators in Non-Standard Function Spaces
Author: Vakhtang KokilashviliPublisher: Birkhäuser
ISBN: 3319210157
Category : Mathematics
Languages : en
Pages : 585
Book Description
This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Bergman's Integral Operator Method in Generalized Axially Symmetric Potential Theory
Author: R. P. GilbertPublisher:
ISBN:
Category :
Languages : en
Pages : 44
Book Description
The solutions of the partial differential equa tion for generalized axially symmetric potentials are investigated by means of integral operators. Results concerning singularities, residues, bounds, and growth are found, which are analogous to those of classical, analytic function theory. (Author).
Potential Theory
Author: Masanori KishiPublisher: Walter de Gruyter
ISBN: 3110859068
Category : Mathematics
Languages : en
Pages : 417
Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Potential Theory - ICPT 94
Author: Josef KralPublisher: Walter de Gruyter
ISBN: 3110818574
Category : Mathematics
Languages : en
Pages : 513
Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Foundations of Potential Theory
Author: Oliver Dimon KelloggPublisher: Read Books Ltd
ISBN: 1446547833
Category : Philosophy
Languages : en
Pages : 329
Book Description
The present volume gives a systematic treatment of potential functions. It takes its origin in two courses, one elementary and one advanced, which the author has given at intervals during the last ten years, and has a two-fold purpose first, to serve as an introduction for students whose attainments in the Calculus include some knowledge of partial derivatives and multiple and line integrals and secondly, to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications, or to - the periodical literature of the day. It is inherent in the nature of the subject that physical intuition and illustration be appealed to freely, and this has been done. However, in order that the ok may present sound ideals to the student, and also serve the mathematician, both for purposes of reference and as a basis for further developments, the proofs have been given by rigorous methods. This has led, at a number of points, to results either not found elsewhere, or not readily accessible. Thus, Chapter IV contains a proof for the general regular region of the divergence theorem Gauss, or Greens theorem on the reduction of volume to surface integrals. The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Pirichlet problem. Exercises are introduced in the conviction that no mastery of a mathematical subject is possible without working with it. They are designed primarily to illustrate or extend the theory, although the desirability of requiring an occasional concrete numerical result has not been lost sight of.
Author: C. Berg