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

Michael Gnewuch

Contact the author: Please use for correspondence this email.
Submission date: 06. Sep. 2005 (revised version: September 2005)
Pages: 27
published in: Colloquium mathematicum, 105 (2006) 1, p. 105-125 
DOI number (of the published article): 10.4064/cm105-1-10
Bibtex
MSC-Numbers: 47A60, 47B25, 22E25, 22E30
Keywords and phrases: spectral multiplier, functional calculus, solvable lie groups
Download full preprint: PDF (280 kB), PS ziped (246 kB)

Abstract:
We consider a special class of sums of non-commuting positive operators on -spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable -functional calculus for . 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.