141 research outputs found
The Levi Decomposition of a Graded Lie Algebra
We show that a graded Lie algebra admits a Levi decomposition that is
compatible with the grading
On derivations of subalgebras of real semisimple Lie algebras
Let g be a real semisimple Lie algebra with Iwasawa decomposition k+a+n.
We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra n that preserves its restricted root space decomposition is of the form ad( W), where W belongs to m+a
Uniformly bounded representations and completely bounded multipliers of SL(2,R)
We estimate the norms of many matrix coefficients of irreducible uniformly
bounded representations of SL(2, R) as completely bounded multipliers of the
Fourier algebra. Our results suggest that the known inequality relating the
uniformly bounded norm of a representation and the completely bounded norm of
its coefficients may not be optimal
Pointwise convergence and semigroups acting on vector-valued functions
A submarkovian C0 semigroup (Tt)t2R+ acting on the
scale of complex-valued functions Lp(X;C) extends to a semigroup of operators on the scale of vector-valued function spaces Lp(X;E), when E is a Banach space. It is known that, if f 2 Lp(X;C), where 1 < p < 1, then Ttf ! f pointwise almost everywhere. We show that the same holds when f 2 Lp(X;E
Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres
A sharp spectral multiplier theorem of Mihlin--H\"ormander type is
proved for a distinguished sub-Laplacian on quaternionic spheres. This is the
first such result on compact sub-Riemannian manifolds where the horizontal
space has corank greater than one. The proof hinges on the analysis of the
quaternionic spherical harmonic decomposition, of which we present an
elementary derivation
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