Smooth Molecular Decompositions Of Functions And Singular Integral Operators PDF Download
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Author | : John E. Gilbert |
Publisher | : American Mathematical Soc. |
Total Pages | : 89 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821827723 |
Download Smooth Molecular Decompositions of Functions and Singular Integral Operators Book in PDF, ePub and Kindle
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
Author | : Shai Dekel |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 250 |
Release | : 2022-04-04 |
Genre | : Mathematics |
ISBN | : 3110761793 |
Download Pointwise Variable Anisotropic Function Spaces on Rn Book in PDF, ePub and Kindle
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.
Author | : Jeffrey A. Hogan |
Publisher | : Springer Science & Business Media |
Total Pages | : 403 |
Release | : 2007-12-21 |
Genre | : Mathematics |
ISBN | : 0817644318 |
Download Time‒Frequency and Time‒Scale Methods Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : Edicions Universitat Barcelona |
Total Pages | : 138 |
Release | : |
Genre | : |
ISBN | : |
Download Collectanea Mathematica Book in PDF, ePub and Kindle
Author | : Heng Sun |
Publisher | : American Mathematical Soc. |
Total Pages | : 79 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821827758 |
Download Spectral Decomposition of a Covering of $GL(r)$: the Borel case Book in PDF, ePub and Kindle
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 ${\bf A}$
Author | : J.S. Byrnes |
Publisher | : Springer Science & Business Media |
Total Pages | : 428 |
Release | : 2001-09-30 |
Genre | : Mathematics |
ISBN | : 9780792371687 |
Download Twentieth Century Harmonic Analysis Book in PDF, ePub and Kindle
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.
Author | : Rodolfo Humberto Torres |
Publisher | : American Mathematical Soc. |
Total Pages | : 185 |
Release | : 1991 |
Genre | : Calderón-Zygmund operator |
ISBN | : 0821825054 |
Download Boundedness Results for Operators with Singular Kernels on Distribution Spaces Book in PDF, ePub and Kindle
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.
Author | : Elias M. Stein |
Publisher | : Princeton University Press |
Total Pages | : 308 |
Release | : 1970 |
Genre | : Mathematics |
ISBN | : 9780691080796 |
Download Singular Integrals and Differentiability Properties of Functions Book in PDF, ePub and Kindle
Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself. Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance. Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.
Author | : Mikhail Anatolʹevich Lifshit︠s︡ |
Publisher | : American Mathematical Soc. |
Total Pages | : 103 |
Release | : 2002 |
Genre | : Computers |
ISBN | : 082182791X |
Download Approximation and Entropy Numbers of Volterra Operators with Application to Brownian Motion Book in PDF, ePub and Kindle
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 $c_1\norm{\rho\psi}_r0$.
Author | : Robert M. Guralnick |
Publisher | : American Mathematical Soc. |
Total Pages | : 96 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821832883 |
Download The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations Book in PDF, ePub and Kindle
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.