Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth
Studia Mathematica, Tome 111 (1994) no. 2, pp. 103-121
We prove that on Iwasawa AN groups coming from arbitrary semisimple Lie groups there is a Laplacian with a nonholomorphic functional calculus, not only for $L^1(AN),$ but also for $L^p(AN)$, where 1 p ∞. This yields a spectral multiplier theorem analogous to the ones known for sublaplacians on stratified groups.
@article{10_4064_sm_111_2_103_121,
author = {Michael Cowling},
title = {Spectral multipliers for a distinguished {Laplacian} on certain groups of exponential growth},
journal = {Studia Mathematica},
pages = {103--121},
year = {1994},
volume = {111},
number = {2},
doi = {10.4064/sm-111-2-103-121},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-111-2-103-121/}
}
TY - JOUR AU - Michael Cowling TI - Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth JO - Studia Mathematica PY - 1994 SP - 103 EP - 121 VL - 111 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-111-2-103-121/ DO - 10.4064/sm-111-2-103-121 LA - en ID - 10_4064_sm_111_2_103_121 ER -
%0 Journal Article %A Michael Cowling %T Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth %J Studia Mathematica %D 1994 %P 103-121 %V 111 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/sm-111-2-103-121/ %R 10.4064/sm-111-2-103-121 %G en %F 10_4064_sm_111_2_103_121
Michael Cowling. Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth. Studia Mathematica, Tome 111 (1994) no. 2, pp. 103-121. doi: 10.4064/sm-111-2-103-121
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