Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth

Michael Cowling; Saverio Giulini; Andrzej Hulanicki; Giancarlo Mauceri

Studia Mathematica (1994)

  • Volume: 111, Issue: 2, page 103-121
  • ISSN: 0039-3223

Abstract

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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 ( A N ) , but also for L p ( A N ) , where 1 < p < ∞. This yields a spectral multiplier theorem analogous to the ones known for sublaplacians on stratified groups.

How to cite

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Cowling, Michael, et al. "Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth." Studia Mathematica 111.2 (1994): 103-121. <http://eudml.org/doc/216123>.

@article{Cowling1994,
abstract = {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.},
author = {Cowling, Michael, Giulini, Saverio, Hulanicki, Andrzej, Mauceri, Giancarlo},
journal = {Studia Mathematica},
keywords = { groups; semisimple Lie groups; spectral multipliers; stratified groups},
language = {eng},
number = {2},
pages = {103-121},
title = {Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth},
url = {http://eudml.org/doc/216123},
volume = {111},
year = {1994},
}

TY - JOUR
AU - Cowling, Michael
AU - Giulini, Saverio
AU - Hulanicki, Andrzej
AU - Mauceri, Giancarlo
TI - Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth
JO - Studia Mathematica
PY - 1994
VL - 111
IS - 2
SP - 103
EP - 121
AB - 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.
LA - eng
KW - groups; semisimple Lie groups; spectral multipliers; stratified groups
UR - http://eudml.org/doc/216123
ER -

References

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