Download or read book Bounded Integral Operators on L 2 Spaces written by P. R. Halmos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something.
Download or read book Bounded Integral Operators on L squared Spaces written by Paul Richard Halmos and published by . This book was released on 1978 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bounded Integral Operators on L written by Paul Richard Halmos and published by . This book was released on 1978 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Aspects of the theory of bounded integral operators in L super p spaces written by George O. Okikiolu and published by . This book was released on 1971 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Aspects of the Theory of Bounded Integral Operators in L spaces written by G. O. Okikiolu and published by . This book was released on 1971 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bounded Integral Operators on L2 Spaces written by Paul Richard Halmos and published by Springer. This book was released on 1978 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Aspects of Theory of Bounded Integral Operators in L p Spaces written by George Olatokunbo Okikiolu and published by . This book was released on 1971 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Aspects of the Theory of Bounded Integral Operators in Lp spaces written by George Olatokunbo Okikiolu and published by . This book was released on 1971 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book L p Boundedness of Fourier Integral Operators written by Michael Beals and published by American Mathematical Soc.. This book was released on 1982 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of Fourier integral operators is shown to be bounded on a range of [italic]L[superscript italic]p spaces depending on the order of the operator. The proof involves calculation of a partial asymptotic expansion for an oscillating integral. The results are applied to solutions of strongly hyperbolic partial differential equations.
Download or read book Bounded and Compact Integral Operators written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book ASPECTS OF THE THEORY OF BOUNDED INTEGRAL OPERATORS IN L P SPACES VON GEORGE OLATOKUNBO written by George O. Okikiolu and published by . This book was released on 1971 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variable Lebesgue Spaces written by David V. Cruz-Uribe and published by Springer Science & Business Media. This book was released on 2013-02-12 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.
Download or read book Singular Integral Operators written by Solomon G. Mikhlin and published by Springer Science & Business Media. This book was released on 1987 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.
Download or read book Bounded Integral Operators on 12 Spaces written by and published by . This book was released on 1978 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singular Integral Operators and Related Topics written by A. Böttcher and published by Birkhäuser. This book was released on 2012-12-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers on modern operator theory and its applications, arising from a joint workshop on linear one-dimensional singular integral equations. The book is of interest to a wide audience in the mathematical and engineering sciences.
Download or read book Introduction to the Theory of Singular Integral Operators with Shift written by Viktor G. Kravchenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the Fredholm theory of singular integral operators with shift in Lp, 1
Download or read book Partial Integral Operators and Integro Differential Equations written by Jurgen Appell and published by CRC Press. This book was released on 2000-02-29 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.
