Abstract
For a system A = (A i ,…, A n ) of linear operators whose real linear combinations have spectra contained in a fixed sector in ℂ and satisfy resolvent bounds there, functions f(A) of the system A of operators can be formed for monogenic functions f having decay at zero and infinity in a corresponding sector in ℝn+1. In the case that the operators A i ,…, A n commute with each other and satisfy square function estimates in Hilbert space, the correspondence between bounded monogenic functions defined in a sector in ℝn+1 and bounded holomorphic functions defined in a sector in ℂn is used to define the functional calculus f→f(A) for bounded holomorphic functions f in a sector of ℂn. The treatment includes the Dirac operator on a Lipschitz surface in ℝn+1.
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© 2004 Birkhäuser Boston
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Jefferies, B. (2004). A Symmetric Functional Calculus for Systems of Operators of Type ω. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_4
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DOI: https://doi.org/10.1007/978-1-4612-2044-2_4
Publisher Name: Birkhäuser Boston
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