Harmonic Analysis on Exponential Solvable Lie Groups by Hidenori Fujiwara & Jean Ludwig

Author:Hidenori Fujiwara & Jean Ludwig
Language: eng
Format: epub
Publisher: Springer Japan, Tokyo

The subspaces are clearly j-invariant. The formulas (7.3.5), (7.3.6) and (7.3.9) show that P 0 is orthogonal to . As in Sect. 2 of [61], we can show that is an ideal of . Now the relations (7.3.5) and (7.3.6) show that and are mutually orthogonal with respect to S. Let u (resp. v) be an eigenvector of ad P jr corresponding to an eigenvalue (resp. ). By (7.3.9),

Hence if μ ≠ ν, it follows that S(u, v) = S(ju, v) = 0. Therefore β(u, v) = 0 and β(jr, [u, v]) = 0. If μ = ν,

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.