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ISSN 1088-6850(e) ISSN 0002-9947(p)

A spectral multiplier theorem for non-self-adjoint operators

Author(s): El Maati Ouhabaz
Journal: Trans. Amer. Math. Soc. 361 (2009), 6567-6582.
MSC (2000): Primary 42B15; Secondary 47F05
Posted: July 17, 2009
MathSciNet review: 2538605
Retrieve article in: PDF

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Abstract: We prove a spectral multiplier theorem for non-self-adjoint operators. More precisely, we consider non-self-adjoint operators $A: D(A) \subset L^2 \to L^2$ having numerical range in a sector $\Sigma(w)$ of angle and whose heat kernel satisfies a Gaussian upper bound. We prove that for every bounded holomorphic function on $\Sigma(w),$ acts on with norm estimated by the behavior of a finite number of derivatives of on the boundary of $\Sigma(w).$

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