We consider -tuples of commuting operators on a Banach space with real spectra. The holomorphic functional calculus for is extended to algebras of ultra-differentiable functions on , depending on the growth of , , when . 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.
@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}, pages = {925--955}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 1}, number = {4}, year = {2002}, mrnumber = {1991008}, zbl = {1099.47505}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2002_5_1_4_925_0/} }
TY - JOUR AU - Andersson, Mats AU - Berndtsson, Bo TI - Non-holomorphic functional calculus for commuting operators with real spectrum JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 925 EP - 955 VL - 1 IS - 4 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2002_5_1_4_925_0/ LA - en ID - ASNSP_2002_5_1_4_925_0 ER -
%0 Journal Article %A Andersson, Mats %A Berndtsson, Bo %T Non-holomorphic functional calculus for commuting operators with real spectrum %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 925-955 %V 1 %N 4 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_2002_5_1_4_925_0/ %G en %F 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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