Author: John E. Gilbert
Publisher: American Mathematical Soc.
ISBN: 0821827723
Category : Mathematics
Languages : en
Pages : 89
Book Description
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
Smooth Molecular Decompositions of Functions and Singular Integral Operators
Author: John E. Gilbert
Publisher: American Mathematical Soc.
ISBN: 0821827723
Category : Mathematics
Languages : en
Pages : 89
Book Description
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
Publisher: American Mathematical Soc.
ISBN: 0821827723
Category : Mathematics
Languages : en
Pages : 89
Book Description
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
Pointwise Variable Anisotropic Function Spaces on Rn
Author: Shai Dekel
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110761793
Category : Mathematics
Languages : en
Pages : 250
Book Description
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.
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110761793
Category : Mathematics
Languages : en
Pages : 250
Book Description
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.
Time‒Frequency and Time‒Scale Methods
Author: Jeffrey A. Hogan
Publisher: Springer Science & Business Media
ISBN: 0817644318
Category : Mathematics
Languages : en
Pages : 403
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 0817644318
Category : Mathematics
Languages : en
Pages : 403
Book Description
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.
Collectanea Mathematica
Author:
Publisher: Edicions Universitat Barcelona
ISBN:
Category :
Languages : en
Pages : 138
Book Description
Publisher: Edicions Universitat Barcelona
ISBN:
Category :
Languages : en
Pages : 138
Book Description
Twentieth Century Harmonic Analysis
Author: J.S. Byrnes
Publisher: Springer Science & Business Media
ISBN: 9780792371687
Category : Mathematics
Languages : en
Pages : 428
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 9780792371687
Category : Mathematics
Languages : en
Pages : 428
Book Description
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.
Boundedness Results for Operators with Singular Kernels on Distribution Spaces
Author: Rodolfo Humberto Torres
Publisher: American Mathematical Soc.
ISBN: 0821825054
Category : Calderón-Zygmund operator
Languages : en
Pages : 185
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 0821825054
Category : Calderón-Zygmund operator
Languages : en
Pages : 185
Book Description
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.
Singular Integrals and Differentiability Properties of Functions
Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 9780691080796
Category : Mathematics
Languages : en
Pages : 308
Book Description
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.
Publisher: Princeton University Press
ISBN: 9780691080796
Category : Mathematics
Languages : en
Pages : 308
Book Description
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.
Approximation and Entropy Numbers of Volterra Operators with Application to Brownian Motion
Author: Mikhail Anatolʹevich Lifshit︠s︡
Publisher: American Mathematical Soc.
ISBN: 082182791X
Category : Computers
Languages : en
Pages : 103
Book Description
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 $c_1\norm{\rho\psi}_r0$.
Publisher: American Mathematical Soc.
ISBN: 082182791X
Category : Computers
Languages : en
Pages : 103
Book Description
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 $c_1\norm{\rho\psi}_r0$.
The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations
Author: Robert M. Guralnick
Publisher: American Mathematical Soc.
ISBN: 0821832883
Category : Mathematics
Languages : en
Pages : 96
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 0821832883
Category : Mathematics
Languages : en
Pages : 96
Book Description
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.
Elliptic Partial Differential Operators and Symplectic Algebra
Author: William Norrie Everitt
Publisher: American Mathematical Soc.
ISBN: 0821832352
Category : Mathematics
Languages : en
Pages : 130
Book Description
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
Publisher: American Mathematical Soc.
ISBN: 0821832352
Category : Mathematics
Languages : en
Pages : 130
Book Description
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