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
Download or read book Time Frequency and Time Scale Methods written by Jeffrey A. Hogan and published by Springer Science & Business Media. This book was released on 2007-12-21 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of these areas are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. "Foundations of Time-Frequency and Time-Scale Methods" will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics.
Download or read book Spectral Decomposition of a Covering of GL r the Borel case written by Heng Sun and published by American Mathematical Soc.. This book was released on 2002 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $F$ be a number field and ${\bf A}$ the ring of adeles over $F$. Suppose $\overline{G({\bf A})}$ is a metaplectic cover of $G({\bf A})=GL(r, {\bf A})$ which is given by the $n$-th Hilbert symbol on ${\bf A}$
Download or read book Collectanea Mathematica written by and published by Edicions Universitat Barcelona. This book was released on with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pointwise Variable Anisotropic Function Spaces on Rn written by Shai Dekel and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-04-04 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spaces of homogeneous type were introduced as a generalization to the Euclidean space and serve as a sufficient setting in which one can generalize the classical isotropic Harmonic analysis and function space theory. This setting is sometimes too general, and the theory is limited. Here, we present a set of flexible ellipsoid covers of Rn that replace the Euclidean balls and support a generalization of the theory with fewer limitations.
Download or read book Twentieth Century Harmonic Analysis written by J.S. Byrnes and published by Springer Science & Business Media. This book was released on 2001-09-30 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated. The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.
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.
Download or read book Approximation and Entropy Numbers of Volterra Operators with Application to Brownian Motion written by Mikhail Anatolʹevich Lifshit︠s︡ and published by American Mathematical Soc.. This book was released on 2002 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text considers a specific Volterra integral operator and investigates its degree of compactness in terms of properties of certain kernel functions. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho, \psi})$ satisfy $c_1\norm{\rho\psi}_r0$.
Download or read book The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations written by Robert M. Guralnick and published by American Mathematical Soc.. This book was released on 2003 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigates the analogous question for rational functions. This book describes the Galois theoretic translation, based on Chebotarev's density theorem, leads to a certain property of permutation groups, called exceptionality.
Download or read book Elliptic Partial Differential Operators and Symplectic Algebra written by William Norrie Everitt and published by American Mathematical Soc.. This book was released on 2003 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This investigation introduces a new description and classification for the set of all self-adjoint operators (not just those defined by differential boundary conditions) which are generated by a linear elliptic partial differential expression $A(\mathbf{x}, D)=\sum_{0\, \leq\, \left s\right \, \leq\,2m}a_{s} (\mathbf{x})D DEGREES{s}\;\text{for all}\;\mathbf{x}\in\Omega$ in a region $\Omega$, with compact closure $\overline{\Omega}$ and $C DEGREES{\infty }$-smooth boundary $\partial\Omega$, in Euclidean space $\mathbb{E} DEGREES{r}$ $(r\geq2).$ The order $2m\geq2$ and the spatial dimensio
Download or read book Basic Global Relative Invariants for Homogeneous Linear Differential Equations written by Roger Chalkley and published by American Mathematical Soc.. This book was released on 2002 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.
Download or read book Some Generalized Kac Moody Algebras with Known Root Multiplicities written by Peter Niemann and published by American Mathematical Soc.. This book was released on 2002 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.
Download or read book Almost Commuting Elements in Compact Lie Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2002 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text describes the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in the extended Dynkin diagram of the simply connected cover, together with the co-root integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.
Download or read book Derived ell Adic Categories for Algebraic Stacks written by Kai Behrend and published by American Mathematical Soc.. This book was released on 2003 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.
Download or read book The Moduli Space of N 1 Superspheres with Tubes and the Sewing Operation written by Katrina Barron and published by American Mathematical Soc.. This book was released on 2003 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic $N = 1$ superconformal field theory, this book defines the moduli space of $N=1$ genus-zero super-Riemann surfaces with oriented and ordered half-infinite tubes, modulo superconformal equivalence.
Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 930 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Central Critical Values of the Degree Four L functions for mathrm GSp 4 The Fundamental Lemma written by Masaaki Furusawa and published by American Mathematical Soc.. This book was released on 2003 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].
