Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth
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DOI: 10.1016/j.jfa.2019.05.024
Abstract: Abstract Let L be a sub-Laplacian on a connected Lie group G of polynomial growth. It is well known that, if F : R → C is in the Schwartz class S ( R )… read more here.
Keywords: kernels versus; groups polynomial; polynomial growth; convolution kernels ... See more keywords
Chevalley groups of polynomial rings over Dedekind domains
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DOI: 10.1515/jgth-2019-0100
Abstract: Abstract Let R be a Dedekind domain and G a split reductive group, i.e. a Chevalley–Demazure group scheme, of rank ≥2{\geq 2}. We prove that G(R[x1,…,xn])=G(R)E(R[x1,…,xn]) for anyn≥1.G(R[x_{1},\ldots,x_{n}])=G(R)E(R[x_{1},\ldots,x_{n}])\quad\text{for any}\ n% \geq 1. In particular, this extends… read more here.
Keywords: groups polynomial; polynomial rings; group; chevalley groups ... See more keywords