[EN] We characterize the wave front set WF*P (u) with respect to the iterates of a linear partial differential operator with constant coefficients of a classical distribution u is an element of D '(Omega), Omega an open ...
[EN] We give a simple proof of a general theorem of Kotake-Narasimhan for elliptic operators in the setting of ultradifferentiable functions in the sense of Braun, Meise and Taylor. We follow the ideas of Komatsu. Based ...
[EN] We introduce a global wave front set using Weyl quantizations of pseudodifferential operators of infinite order in the ultradifferentiable setting. We see that in many cases it coincides with the Gabor wave front set ...
[EN] Given a function f E L2, we consider means and variances associated to f and its Fourier transform
, and explore their relations with the Wigner transform W(f), obtaining, as particular cases, a simple new proof of ...
[EN] We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient ...
[EN] We use techniques from time-frequency analysis to show that the space S(omega )of rapidly decreasing omega-ultradifferentiable functions is nuclear for every weight function omega(t) = o(t) as t tends to infinity. ...
[EN] We develop real Paley-Wiener theorems for classes S-omega of ultradifferentiable functions and related L-p-spaces in the spirit of Bang and Andersen for the Schwartz class. We introduce results of this type for the ...
[EN] We study the behaviour of linear partial differential operators with polynomial coefficients via a Wigner type transform. In particular, we obtain some results of regularity in the Schwartz space $\Sch$ and in the ...
[EN] We consider the spaces of ultradifferentiable functions S as introduced by Bjorck (and its dual S) and we use time-frequency analysis to define a suitable wave front set in this setting and obtain several applications: ...