Differentiable $L^p$-functional calculus for certain sums of non-commuting operators

Michael Gnewuch. "Differentiable $L^{p}$-functional calculus for certain sums of non-commuting operators." Colloquium Mathematicae 105.1 (2006): 105-125. <http://eudml.org/doc/283794>.

@article{MichaelGnewuch2006,
abstract = {We consider a special class of sums of non-commuting positive operators on L²-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable $L^\{p\}$-functional calculus for 1 ≤ p ≤ ∞. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.},
author = {Michael Gnewuch},
journal = {Colloquium Mathematicae},
keywords = {selfadjointness; differential functional calculus; holomorphic semigroup; spectral multiplier; solvable Lie group; exponential volume growth; sub-Laplacian; Schrödinger operator; sum of even powers of vector fields},
language = {eng},
number = {1},
pages = {105-125},
title = {Differentiable $L^\{p\}$-functional calculus for certain sums of non-commuting operators},
url = {http://eudml.org/doc/283794},
volume = {105},
year = {2006},
}

TY - JOUR
AU - Michael Gnewuch
TI - Differentiable $L^{p}$-functional calculus for certain sums of non-commuting operators
JO - Colloquium Mathematicae
PY - 2006
VL - 105
IS - 1
SP - 105
EP - 125
AB - We consider a special class of sums of non-commuting positive operators on L²-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable $L^{p}$-functional calculus for 1 ≤ p ≤ ∞. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.
LA - eng
KW - selfadjointness; differential functional calculus; holomorphic semigroup; spectral multiplier; solvable Lie group; exponential volume growth; sub-Laplacian; Schrödinger operator; sum of even powers of vector fields
UR - http://eudml.org/doc/283794
ER -