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, p. 925-955
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 n , depending on the growth of exp(ia·t), t n , when |t|. 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.
Classification:  47A60,  47A13,  32A25,  32A65,  46F05
@article{ASNSP_2002_5_1_4_925_0,
     author = {Andersson, Mats and Berndtsson, Bo},
     title = {Non-holomorphic functional calculus for commuting operators with real spectrum},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {4},
     year = {2002},
     pages = {925-955},
     zbl = {1099.47505},
     mrnumber = {1991008},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_4_925_0}
}
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. http://www.numdam.org/item/ASNSP_2002_5_1_4_925_0/

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