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LEADER: 02922nam a22004815a 4500
001 013839657-4
005 20131206201141.0
008 121227s2004 xxu| s ||0| 0|eng d
020 $a9780817681647
020 $a9780817681647
020 $a9781461264682
024 7 $a10.1007/978-0-8176-8164-7$2doi
035 $a(Springer)9780817681647
040 $aSpringer
050 4 $aQA403-403.3
072 7 $aPBKD$2bicssc
072 7 $aMAT034000$2bisacsh
082 04 $a515.785$223
100 1 $aThangavelu, Sundaram,$eauthor.
245 13 $aAn Introduction to the Uncertainty Principle :$bHardy’s Theorem on Lie Groups /$cby Sundaram Thangavelu.
264 1 $aBoston, MA :$bBirkhäuser Boston :$bImprint: Birkhäuser,$c2004.
300 $aXIII, 174 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aProgress in Mathematics ;$v217
505 0 $aForeword (G. Folland) -- Preface -- Euclidean Spaces -- Heisenberg Groups -- Symmetric Spaces of Rank one -- Bibliography -- Index.
520 $aMotivating this interesting monograph is the development of a number of analogs of Hardy's theorem in settings arising from noncommutative harmonic analysis. This is the central theme of this work. Specifically, it is devoted to connections among various theories arising from abstract harmonic analysis, concrete hard analysis, Lie theory, special functions, and the very interesting 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 second chapter establishes several versions of Hardy's theorem for the Fourier transform on the Heisenberg group and characterizes the heat kernel 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 such as representation theory, spherical functions, Hecke-Bochner formulas and special functions. Graduate students and researchers in harmonic analysis will greatly benefit from this book.
650 20 $aFunctional analysis.
650 20 $aFourier analysis.
650 10 $aMathematics.
650 0 $aMathematics.
650 0 $aHarmonic analysis.
650 0 $aFourier analysis.
650 0 $aFunctional analysis.
650 0 $aDifferential equations, partial.
650 24 $aAbstract Harmonic Analysis.
650 24 $aSeveral Complex Variables and Analytic Spaces.
776 08 $iPrinted edition:$z9781461264682
830 0 $aProgress in Mathematics ;$v217.
988 $a20131119
906 $0VEN