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Boundedness Results For Operators With Singular Kernels On Distribution Spaces
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Book Synopsis Boundedness Results for Operators with Singular Kernels on Distribution Spaces by : Rodolfo Humberto Torres
Download or read book Boundedness Results for Operators with Singular Kernels on Distribution Spaces written by Rodolfo Humberto Torres and published by . This book was released on 1991 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boundedness Results for Operators with Singular Kernels on Distribution Spaces by : Rodolfo Humberto Torres
Download or read book Boundedness Results for Operators with Singular Kernels on Distribution Spaces written by Rodolfo Humberto Torres and published by American Mathematical Soc.. This book was released on 1991 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete decomposition techniques for spaces for functions or distributions are very useful tools for studying many problems in analysis. In this work, the author uses this type of decomposition, associated with the so-called *p-transform and wavelet-transform theories, to analyse a large class of operators, including pseudodifferential operators, Calderon-Zygmund operators, and other operators with singular kernels. The methods used combine Littlewood-Paley type characterizations of spaces of distributions with certain atomic and molecular decompositions. In this way, the study of operators on most of the classical function spaces - such as Hardy spaces, Besov-Lipschitz spaces, and Sobolev spaces - can be accomplished in a unified manner. The book is written in an expository style that makes it suitable for advanced graduate students in analysis.
Book Synopsis Boundedness Results for Operators with Singular Kernels on Distribution Spaces by : Rodolfo Humberto Torres
Download or read book Boundedness Results for Operators with Singular Kernels on Distribution Spaces written by Rodolfo Humberto Torres and published by American Mathematical Soc.. This book was released on 1991 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the author generalizes the T1 theorem of G. David and J.-L. Journé to the context of Triebel-Lizorkin spaces, which include most of the function and distribution spaces of importance in classical analysis. M. Frazier and B. Jawerth have shown that these spaces admit decompositions in terms of certain fundamental building blocks, known as "smooth atoms'' and "smooth molecules''. In the author's words, "to prove that an operator is bounded on a Triebel-Lizorkin space, it is enough to show that it maps every family of smooth atoms into a family of smooth molecules''. The same basic techniques can be used to study operators between two different Triebel-Lizorkin spaces. Results are obtained for a wide variety of operators acting on the Triebel-Lizorkin spaces, including generalized Calderón-Zygmund operators and their derivatives; potential operators; fractional integral operators; and the Hörmander classes of pseudodifferential operators. When these general results are restricted to specific spaces, many classical boundedness results are recovered.
Book Synopsis Kernel Functions, Analytic Torsion, and Moduli Spaces by : John D. Fay
Download or read book Kernel Functions, Analytic Torsion, and Moduli Spaces written by John D. Fay and published by American Mathematical Soc.. This book was released on 1992 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work investigates analytic torsion on the moduli space of degree zero stable bundles on a compact Reimann surface. Zeta-function regularization and perturbation-curvature formulas for torsion are developed using a modified resolvent-Szego kernel. The author discusses the bosonization formulas of mathematical physics. Riemann vanishing theorems for torsion, and analytic properties (insertion-residue formulas and heat equations) for the nonabelian theta function and Szego kernel. In addition, he provides background material on bundle-moduli spaces, Quillen metrics, and theta functions.
Book Synopsis Morrey and Campanato Meet Besov, Lizorkin and Triebel by : Wen Yuan
Download or read book Morrey and Campanato Meet Besov, Lizorkin and Triebel written by Wen Yuan and published by Springer Science & Business Media. This book was released on 2010-09-18 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.
Book Synopsis Modern Fourier Analysis by : Loukas Grafakos
Download or read book Modern Fourier Analysis written by Loukas Grafakos and published by Springer. This book was released on 2014-11-13 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is aimed at graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary.
Book Synopsis Smooth Molecular Decompositions of Functions and Singular Integral Operators by : John E. Gilbert
Download or read book Smooth Molecular Decompositions of Functions and Singular Integral Operators written by John E. Gilbert and published by American Mathematical Soc.. This book was released on 2002 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under minimal assumptions on a function $\psi$ the authors obtain wavelet-type frames of the form $\psi_{j, k}(x) = r DEGREES{(1/2)n j} \psi(r DEGREESj x - sk), j \in \integer, k \in \integer DEGREESn, $ for some $r > 1$ and $s > 0$. This collection is shown to be a frame for a scale of Triebel-Lizorkin spaces (which includes Lebesgue, Sobolev and Hardy spaces) and the reproducing formula converges in norm as well as pointwise a.e. The construction follows from a characterization of those operators which are bounded on a space of smooth molecules. This characterization also allows us to decompose a broad range of singular integral operators in ter
Book Synopsis Littlewood-Paley Theory and the Study of Function Spaces by : Michael Frazier
Download or read book Littlewood-Paley Theory and the Study of Function Spaces written by Michael Frazier and published by American Mathematical Soc.. This book was released on 1991 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Littlewood-Paley theory was developed to study function spaces in harmonic analysis and partial differential equations. Recently, it has contributed to the development of the *q-transform and wavelet decompositions. Based on lectures presented at the NSF-CBMS Regional Research Conference on Harmonic Analysis and Function Spaces, held at Auburn University in July 1989, this book is aimed at mathematicians, as well as mathematically literate scientists and engineers interested in harmonic analysis or wavelets. The authors provide not only a general understanding of the area of harmonic analysis relating to Littlewood-Paley theory and atomic and wavelet decompositions, but also some motivation and background helpful in understanding the recent theory of wavelets. The book begins with some simple examples which provide an overview of the classical Littlewood-Paley theory. The *q-transform, wavelet, and smooth atomic expansions are presented as natural extensions of the classical theory. Finally, applications to harmonic analysis (Calderon-Zygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.
Book Synopsis Wavelet Theory by : Igor Iakovlevič Novikov (mathématicien).)
Download or read book Wavelet Theory written by Igor Iakovlevič Novikov (mathématicien).) and published by American Mathematical Soc.. This book was released on 2011 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet theory lies on the crossroad of pure and computational mathematics, with connections to audio and video signal processing, data compression, and information transmission. The present book is devoted to a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies their structural and approximation properties, starting with basic theory and ending with special topics and problems. The book also presents some applications of wavelets. Historical commentary is supplied for each chapter in the book, and most chapters contain exercises. The book is intended for professional mathematicians and graduate students working in functional analysis and approximation theory. It is also useful for engineers applying wavelet theory in their work. Prerequisites for reading the book consist of graduate courses in real and functional analysis.
Book Synopsis Lattice Structures on Banach Spaces by : Nigel John Kalton
Download or read book Lattice Structures on Banach Spaces written by Nigel John Kalton and published by American Mathematical Soc.. This book was released on 1993 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general problem addressed in this work is to characterize the possible Banach lattice structures that a separable Banach space may have. The basic questions of uniqueness of lattice structure for function spaces have been studied before, but here the approach uses random measure representations for operators in a new way to obtain more powerful conclusions. A typical result is the following: If $X$ is a rearrangement-invariant space on $[0,1]$ not equal to $L_2$, and if $Y$ is an order-continuous Banach lattice which has a complemented subspace isomorphic as a Banach space to $X$, then $Y$ has a complemented sublattice which is isomorphic to $X$ (with one of two possible lattice structures). New examples are also given of spaces with a unique lattice structure.
Book Synopsis Coarse Cohomology and Index Theory on Complete Riemannian Manifolds by : John Roe
Download or read book Coarse Cohomology and Index Theory on Complete Riemannian Manifolds written by John Roe and published by American Mathematical Soc.. This book was released on 1993 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: ``Coarse geometry'' is the study of metric spaces from the asymptotic point of view: two metric spaces (such as the integers and the real numbers) which ``look the same from a great distance'' are considered to be equivalent. This book develops a cohomology theory appropriate to coarse geometry. The theory is then used to construct ``higher indices'' for elliptic operators on noncompact complete Riemannian manifolds. Such an elliptic operator has an index in the $K$-theory of a certain operator algebra naturally associated to the coarse structure, and this $K$-theory then pairs with the coarse cohomology. The higher indices can be calculated in topological terms thanks to the work of Connes and Moscovici. They can also be interpreted in terms of the $K$-homology of an ideal boundary naturally associated to the coarse structure. Applications to geometry are given, and the book concludes with a discussion of the coarse analog of the Novikov conjecture.
Book Synopsis Gorenstein Quotient Singularities in Dimension Three by : Stephen Shing-Toung Yau
Download or read book Gorenstein Quotient Singularities in Dimension Three written by Stephen Shing-Toung Yau and published by American Mathematical Soc.. This book was released on 1993 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: If $G$ is a finite subgroup of $G\!L(3,{\mathbb C})$, then $G$ acts on ${\mathbb C}^3$, and it is known that ${\mathbb C}^3/G$ is Gorenstein if and only if $G$ is a subgroup of $S\!L(3,{\mathbb C})$. In this work, the authors begin with a classification of finite subgroups of $S\!L(3,{\mathbb C})$, including two types, (J) and (K), which have often been overlooked. They go on to present a general method for finding invariant polynomials and their relations to finite subgroups of $G\!L(3,{\mathbb C})$. The method is, in practice, substantially better than the classical method due to Noether. Some properties of quotient varieties are presented, along with a proof that ${\mathbb C}^3/G$ has isolated singularities if and only if $G$ is abelian and 1 is not an eigenvalue of $g$ for every nontrivial $g \in G$. The authors also find minimal quotient generators of the ring of invariant polynomials and relations among them.
Book Synopsis Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields by : Oscar Zariski
Download or read book Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields written by Oscar Zariski and published by American Mathematical Soc.. This book was released on 1951 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extension of Positive-Definite Distributions and Maximum Entropy by : Jean-Pierre Gabardo
Download or read book Extension of Positive-Definite Distributions and Maximum Entropy written by Jean-Pierre Gabardo and published by American Mathematical Soc.. This book was released on 1993 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.
Book Synopsis Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace by : Steven Zelditch
Download or read book Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace written by Steven Zelditch and published by American Mathematical Soc.. This book was released on 1992 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is concerned with a pair of dual asymptotics problems on a finite-area hyperbolic surface. The first problem is to determine the distribution of closed geodesics in the unit tangent bundle. The second problem is to determine the distribution of eigenfunctions (in microlocal sense) in the unit tangent bundle.
Book Synopsis Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory by : David Soudry
Download or read book Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory written by David Soudry and published by American Mathematical Soc.. This book was released on 1993 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work studies the local theory for certain Rankin-Selberg convolutions for the standard $L$-function of degree $21n$ of generic representations of $\textnormal{SO}_{2\ell +1}(F)\times \textnormal{GL}_n(F)$ over a local field $F$. The local integrals converge in a half-plane and continue meromorphically to the whole plane. One main result is the existence of local gamma and $L$-factors. The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals. In addition, Soudry establishes the multiplicativity of the gamma factor ($1
Book Synopsis Invariant Subsemigroups of Lie Groups by : Karl-Hermann Neeb
Download or read book Invariant Subsemigroups of Lie Groups written by Karl-Hermann Neeb and published by American Mathematical Soc.. This book was released on 1993 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the first systematic treatment of invariant Lie semi groups. Because these semi groups provide interesting models for space times in general relativity, this work will be useful to both mathematicians and physicists. It will also appeal to engineers interested in bi-invariant control systems on Lie groups. Neeb investigates closed invariant subsemigroups of Lie groups which are generated by one-parameter semi groups and the sets of infinitesimal generators of such semi groups - invariant convex cones in Lie algebras.In addition, a characterization of those finite-dimensional real Lie algebras containing such cones is obtained. The global part of the theory deals with globality problems (Lie's third theorem for semi groups), controllability problems, and the facial structure of Lie semi groups. Neeb also determines the structure of the universal compactification of an invariant Lie semigroup and shows that the lattice of idempotents is isomorphic to a lattice of faces of the cone dual to the cone of infinitesimal generators.
