Non-holomorphic functional calculus for commuting operators with real spectrum

Andersson, Mats ; Berndtsson, Bo

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 4, pp. 925-955

Résumé

We consider $n$-tuples of commuting operators $a=a_1,...,a_n$ on a Banach space with real spectra. The holomorphic functional calculus for $a$ is extended to algebras of ultra-differentiable functions on ${ℝ}^n$, depending on the growth of $\parallel exp(ia·t)\parallel$, $t\in {ℝ}^n$, when $\left|t\right|\to \infty$. In the non-quasi-analytic case we use the usual Fourier transform, whereas for the quasi-analytic case we introduce a variant of the FBI transform, adapted to ultradifferentiable classes.

Détail

Classification : 47A60, 47A13, 32A25, 32A65, 46F05