Negative results on the Nash-Moser theorem for Köthe sequences spaces and for spaces of ultradifferentiable functions.
New characterizations for Hankel transformable spaces of Zemanian.
Non-holomorphic functional calculus for commuting operators with real spectrum
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.
Nonlinear maps in spaces of distributions.
Non-Standard Analysis And Generalized Functions.
Normal operators spaces of distributions.