04033nam a22005535i 4500001001800000003000900018005001700027007001500044008004100059020001800100024002500118050001200143050001000155072001600165072002300181072002300204082001500227082001600242245015600258264004600414300004400460336002600504337002600530338003600556347002400592490003500616505022300651520201800874650001702892650001802909650002402927650001602951650002302967650003602990650002703026650001703053650003603070650003203106650002703138650005103165650003803216700003503254700002703289710003403316773002003350776003603370830003503406856003803441978-0-8176-4426-0DE-He21320180115171431.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97808176442607 a10.1007/b1388652doi 4aQA252.3 4aQA387 7aPBG2bicssc 7aMAT0140002bisacsh 7aMAT0380002bisacsh04a512.5522304a512.48222310aLie Theoryh[electronic resource] :bHarmonic Analysis on Symmetric Spaces—General Plancherel Theorems /cedited by Jean-Philippe Anker, Bent Orsted. 1aBoston, MA :bBirkhäuser Boston,c2005. aVIII, 175 p. 3 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aProgress in Mathematics ;v2300 aThe Plancherel Theorem for a Reductive Symmetric Space -- The Paley—Wiener Theorem for a Reductive Symmetric Space -- The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space. aSemisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. Harmonic Analysis on Symmetric Spaces—General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces. Van den Ban’s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass–Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley–Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals. Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology, Harmonic Analysis on Symmetric Spaces—General Plancherel Theorems provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required. 0aMathematics. 0aGroup theory. 0aTopological groups. 0aLie groups. 0aHarmonic analysis. 0aFunctions of complex variables. 0aDifferential geometry.14aMathematics.24aTopological Groups, Lie Groups.24aAbstract Harmonic Analysis.24aDifferential Geometry.24aSeveral Complex Variables and Analytic Spaces.24aGroup Theory and Generalizations.1 aAnker, Jean-Philippe.eeditor.1 aOrsted, Bent.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817637774 0aProgress in Mathematics ;v23040uhttp://dx.doi.org/10.1007/b138865