Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28

Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28

Author: Gerald B. Folland

Publisher: Princeton University Press

Published: 2020-12-08

Total Pages: 302

ISBN-13: 0691222452

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The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.


Book Synopsis Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 by : Gerald B. Folland

Download or read book Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 written by Gerald B. Folland and published by Princeton University Press. This book was released on 2020-12-08 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

Hardy Spaces on Homogeneous Groups

Hardy Spaces on Homogeneous Groups

Author: Gerald B. Folland

Publisher: Princeton University Press

Published: 1982-06-21

Total Pages: 302

ISBN-13: 9780691083100

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The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.


Book Synopsis Hardy Spaces on Homogeneous Groups by : Gerald B. Folland

Download or read book Hardy Spaces on Homogeneous Groups written by Gerald B. Folland and published by Princeton University Press. This book was released on 1982-06-21 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

Hardy Spaces on Homogeneous Groups

Hardy Spaces on Homogeneous Groups

Author: Gerald B. Folland

Publisher:

Published: 1982

Total Pages: 284

ISBN-13:

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Book Synopsis Hardy Spaces on Homogeneous Groups by : Gerald B. Folland

Download or read book Hardy Spaces on Homogeneous Groups written by Gerald B. Folland and published by . This book was released on 1982 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The American Mathematical Monthly

The American Mathematical Monthly

Author:

Publisher:

Published: 1983

Total Pages: 396

ISBN-13:

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Book Synopsis The American Mathematical Monthly by :

Download or read book The American Mathematical Monthly written by and published by . This book was released on 1983 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tata Lectures on Theta I

Tata Lectures on Theta I

Author: David Mumford

Publisher: Springer Science & Business Media

Published: 2007-06-25

Total Pages: 248

ISBN-13: 0817645772

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This volume is the first of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).


Book Synopsis Tata Lectures on Theta I by : David Mumford

Download or read book Tata Lectures on Theta I written by David Mumford and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).

Advanced Calculus

Advanced Calculus

Author: Lynn Harold Loomis

Publisher: World Scientific Publishing Company

Published: 2014-02-26

Total Pages: 596

ISBN-13: 9814583952

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An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.


Book Synopsis Advanced Calculus by : Lynn Harold Loomis

Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Introduction to Partial Differential Equations

Introduction to Partial Differential Equations

Author: Gerald B. Folland

Publisher: Princeton University Press

Published: 2020-05-05

Total Pages: 340

ISBN-13: 0691213038

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The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers. This book includes many more exercises than the first edition, offers a new chapter on pseudodifferential operators, and contains additional material throughout. The first five chapters of the book deal with classical theory: first-order equations, local existence theorems, and an extensive discussion of the fundamental differential equations of mathematical physics. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics. The last three chapters introduce the modern theory: Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators.


Book Synopsis Introduction to Partial Differential Equations by : Gerald B. Folland

Download or read book Introduction to Partial Differential Equations written by Gerald B. Folland and published by Princeton University Press. This book was released on 2020-05-05 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers. This book includes many more exercises than the first edition, offers a new chapter on pseudodifferential operators, and contains additional material throughout. The first five chapters of the book deal with classical theory: first-order equations, local existence theorems, and an extensive discussion of the fundamental differential equations of mathematical physics. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics. The last three chapters introduce the modern theory: Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators.

Anisotropic Hardy Spaces and Wavelets

Anisotropic Hardy Spaces and Wavelets

Author: Marcin Bownik

Publisher: American Mathematical Soc.

Published: 2003-05-30

Total Pages: 140

ISBN-13: 9780821865033

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In this paper, motivated in part by the role of discrete groups of dilations in wavelet theory, we introduce and investigate the anisotropic Hardy spaces associated with very general discrete groups of dilations. This formulation includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky. Given a dilation $A$, that is an $n\times n$ matrix all of whose eigenvalues $\lambda$ satisfy $|\lambda|>1$, define the radial maximal function $$M^0_\varphi f(x): = \sup_{k\in\mathbb{Z}} |(f*\varphi_k)(x)|, \qquad\text{where } \varphi_k(x) = |\det A|^{-k} \varphi(A^{-k}x).$$ Here $\varphi$ is any test function in the Schwartz class with $\int \varphi \not =0$. For $0


Book Synopsis Anisotropic Hardy Spaces and Wavelets by : Marcin Bownik

Download or read book Anisotropic Hardy Spaces and Wavelets written by Marcin Bownik and published by American Mathematical Soc.. This book was released on 2003-05-30 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, motivated in part by the role of discrete groups of dilations in wavelet theory, we introduce and investigate the anisotropic Hardy spaces associated with very general discrete groups of dilations. This formulation includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky. Given a dilation $A$, that is an $n\times n$ matrix all of whose eigenvalues $\lambda$ satisfy $|\lambda|>1$, define the radial maximal function $$M^0_\varphi f(x): = \sup_{k\in\mathbb{Z}} |(f*\varphi_k)(x)|, \qquad\text{where } \varphi_k(x) = |\det A|^{-k} \varphi(A^{-k}x).$$ Here $\varphi$ is any test function in the Schwartz class with $\int \varphi \not =0$. For $0

Dynamics and Analytic Number Theory

Dynamics and Analytic Number Theory

Author: Dzmitry Badziahin

Publisher: Cambridge University Press

Published: 2016-11-10

Total Pages: 341

ISBN-13: 1316817776

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Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.


Book Synopsis Dynamics and Analytic Number Theory by : Dzmitry Badziahin

Download or read book Dynamics and Analytic Number Theory written by Dzmitry Badziahin and published by Cambridge University Press. This book was released on 2016-11-10 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.

St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

Author:

Publisher:

Published: 2004

Total Pages: 524

ISBN-13:

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Book Synopsis St. Petersburg Mathematical Journal by :

Download or read book St. Petersburg Mathematical Journal written by and published by . This book was released on 2004 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: