MARC Record from marc_columbia

LEADER: 03194cam a2200385 a 4500
001 4202522
005 20221027054211.0
008 030508s2003 mau b 001 0 eng
010 $a 2003050228
020 $a0817643303 (alk. paper)
020 $a3764343303 (alk. paper)
035 $a(OCoLC)52232224
035 $a(OCoLC)ocm52232224
035 $a(NNC)4202522
035 $a4202522
040 $aDLC$cDLC$dOrLoB-B
042 $apcc
050 00 $aQA403$b.T52 2003
082 00 $a512/.55$221
100 1 $aThangavelu, Sundaram.$0http://id.loc.gov/authorities/names/n85294210
245 13 $aAn introduction to the uncertainty principle :$bHardy's theorem on Lie groups /$cSundaram Thangavelu.
260 $aBoston :$bBirkhäuser,$c2003.
300 $axii, 174 pages ;$c25 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aProgress in mathematics ;$vv. 217
504 $aIncludes bibliographical references and index.
505 00 $g1.$tEuclidean Spaces --$g2.$tHeisenberg Groups --$g3.$tSymmetric Spaces of Rank 1.
520 1 $a"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 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: 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."--BOOK JACKET.
650 0 $aHarmonic analysis.$0http://id.loc.gov/authorities/subjects/sh85058939
650 0 $aHomogeneous spaces.$0http://id.loc.gov/authorities/subjects/sh85061766
650 0 $aLie groups.$0http://id.loc.gov/authorities/subjects/sh85076786
650 0 $aHeisenberg uncertainty principle.$0http://id.loc.gov/authorities/subjects/sh85059968
830 0 $aProgress in mathematics (Boston, Mass.) ;$vv. 217.$0http://id.loc.gov/authorities/names/n42019868
852 00 $bmat$hQA403$i.T52 2003