Non-holomorphic functional calculus for commuting operators with real spectrum

Andersson, Mats; Berndtsson, Bo

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 $∥ exp (i a \cdot t) ∥$ , $t \in ℝ^{n}$ , when $| t | \to \infty$ . 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.

MR Zbl | 1 citation dans Numdam

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

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Andersson, Mats; Berndtsson, Bo. Non-holomorphic functional calculus for commuting operators with real spectrum. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 4, pp. 925-955. https://www.numdam.org/item/ASNSP_2002_5_1_4_925_0/

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