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Parameter-ellipticity with respect to a closed subsector of the complex planefor pseudodifferential Douglis-Nirenberg systems is discussed and shown toimply the existence of a bounded H_\infty-calculus in suitable scales ofSobolev, Besov, and Hoelder spaces. We also admit non pseudodifferentialperturbations. Applications concern systems with coefficients of mild Hoelderregularity and the generalized thermoelastic plate equations.

Bounded H_\infty-calculus for pseudodifferential Douglis-Nirenberg systems of mild regularity