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- catalog abstract ""The central theme and motivation of this monograph is the development of analogs of Hardy's Theorem in settings that arise from noncommutative harmonic analysis. Specifically, the book is devoted in part to variations of the mathematical Uncertainty Principle - Hardy's Theorem is one interpretation - which states that a function and its Fourier transform cannot simultaneously be very small. However, this text goes well beyond Hardy-type theorems to develop deeper connections among the fields of abstract harmonic analysis, concrete hard analysis, Lie theory, and special functions, and to study the fascinating interplay between the noncompact groups that underlie the geometric objects in question and the compact rotation groups that act as symmetries of these objects." "A tutorial introduction is given to the necessary background material. The first chapter deals with theorems of Hardy and Beurling for the Euclidean Fourier transform; the second chapter establishes several versions of Hardy's Theorem for the Fourier transform on the Heisenberg group and characterizes the heat kernal for the sublaplacian. In Chapter three, the Helgason Fourier transform on rank one symmetric spaces is treated. Most of the results presented here are valid in the general context of solvable extensions of H-type groups." "The techniques used to prove the main results run the gamut of modern harmonic analysis: they include representation theory, spherical functions, Hecke-Bochner formulas and special functions. Graduate students and researchers in harmonic analysis will benefit from this unique work."--Jacket.".
- catalog alternative "Hardy's theorem on Lie groups".
- catalog contributor b12990699.
- catalog created "c2004.".
- catalog date "2004".
- catalog date "c2004.".
- catalog dateCopyrighted "c2004.".
- catalog description ""A tutorial introduction is given to the necessary background material. The first chapter deals with theorems of Hardy and Beurling for the Euclidean Fourier transform; the second chapter establishes several versions of Hardy's Theorem for the Fourier transform on the Heisenberg group and characterizes the heat kernal for the sublaplacian. In Chapter three, the Helgason Fourier transform on rank one symmetric spaces is treated. Most of the results presented here are valid in the general context of solvable extensions of H-type groups."".
- catalog description ""The central theme and motivation of this monograph is the development of analogs of Hardy's Theorem in settings that arise from noncommutative harmonic analysis. Specifically, the book is devoted in part to variations of the mathematical Uncertainty Principle - Hardy's Theorem is one interpretation - which states that a function and its Fourier transform cannot simultaneously be very small.".
- catalog description ""The techniques used to prove the main results run the gamut of modern harmonic analysis: they include representation theory, spherical functions, Hecke-Bochner formulas and special functions. Graduate students and researchers in harmonic analysis will benefit from this unique work."--Jacket.".
- catalog description "1. Euclidean Spaces -- 2. Heisenberg Groups -- 3. Symmetric Spaces of Rank 1.".
- catalog description "However, this text goes well beyond Hardy-type theorems to develop deeper connections among the fields of abstract harmonic analysis, concrete hard analysis, Lie theory, and special functions, and to study the fascinating interplay between the noncompact groups that underlie the geometric objects in question and the compact rotation groups that act as symmetries of these objects."".
- catalog description "Includes bibliographical references (p. [169]-172) and index.".
- catalog extent "xii, 174 p. ;".
- catalog hasFormat "Introduction to the uncertainty principle.".
- catalog identifier "0817643303 (alk. paper)".
- catalog identifier "3764343303 (alk. paper)".
- catalog isFormatOf "Introduction to the uncertainty principle.".
- catalog isPartOf "Progress in mathematics (Boston, Mass.) ; v. 217.".
- catalog isPartOf "Progress in mathematics ; v. 217".
- catalog issued "2004".
- catalog issued "c2004.".
- catalog language "eng".
- catalog publisher "Boston : Birkhäuser,".
- catalog relation "Introduction to the uncertainty principle.".
- catalog subject "512/.55 21".
- catalog subject "Harmonic analysis.".
- catalog subject "Homogeneous spaces.".
- catalog subject "Lie groups.".
- catalog subject "QA403 .T52 2004".
- catalog tableOfContents "1. Euclidean Spaces -- 2. Heisenberg Groups -- 3. Symmetric Spaces of Rank 1.".
- catalog title "An introduction to the uncertainty principle : Hardy's theorem on Lie groups / Sundaram Thangavelu.".
- catalog title "Hardy's theorem on Lie groups".
- catalog type "text".