By Erik P. van den Ban (auth.), Jean-Philippe Anker, Bent Orsted (eds.)
Semisimple Lie teams, and their algebraic analogues over fields except the reals, are of primary value in geometry, research, and mathematical physics. 3 autonomous, self-contained volumes, lower than the final name Lie Theory, function survey paintings and unique effects by means of well-established researchers in key components of semisimple Lie theory.
Harmonic research on Symmetric Spaces—General Plancherel Theorems offers huge surveys through E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the impressive growth during the last decade in deriving the Plancherel theorem on reductive symmetric spaces.
Van den Ban’s introductory bankruptcy explains the elemental setup of a reductive symmetric area besides a cautious examine of the constitution idea, quite for the hoop of invariant differential operators for the correct classification of parabolic subgroups. complicated themes for the formula and realizing of the facts are lined, together with Eisenstein integrals, regularity theorems, Maass–Selberg kin, and residue calculus for root platforms. Schlichtkrull presents a cogent account of the elemental elements within the harmonic research on a symmetric house in the course of the clarification and definition of the Paley–Wiener theorem. impending the Plancherel theorem via an alternate point of view, the Schwartz area, Delorme bases his dialogue and evidence on asymptotic expansions of eigenfunctions and the idea of intertwining integrals.
Well fitted to either graduate scholars and researchers in semisimple Lie thought and neighboring fields, potentially even mathematical cosmology, Harmonic research on Symmetric Spaces—General Plancherel Theorems offers a extensive, essentially concentrated exam of semisimple Lie teams and their essential value and functions to investigate in lots of branches of arithmetic and physics. wisdom of easy illustration concept of Lie teams in addition to familiarity with semisimple Lie teams, symmetric areas, and parabolic subgroups is required.