We perform Wigner analysis of linear operators. Namely, the standard time-frequency
representation Short-time Fourier Transform (STFT) is replaced by the A-Wigner distribution …

We study an anisotropic version of the Shubin calculus of pseudodifferential operators on R
d. Anisotropic symbols and Gabor wave front sets are defined in terms of decay or growth …

This thesis consists of eight chapters and two appendices. Chapter 1 grants an overview
over the main results. Thereafter, in Chapter 2 the notation is fixed, the operators are …

We perform a phase space analysis of evolution equations associated with the Weyl
quantization $ q^{\mathrm {w}} $ of a complex quadratic form $ q $ on $\mathbb {R}^{2d} …

We prove boundedness results on modulation and Wiener amalgam spaces for some
families of spectral multipliers for the twisted Laplacian. We exploit the metaplectic …

We study the propagation in time of 1/2-Gelfand-Shilov singularities, ie global analytic
singularities, of tempered distributional solutions of the initial value problem {u t+ qw (x, D) …

In this paper we introduce and study global wave front sets in terms of the τ-Wigner
transform in global ultradifferentiable classes of Beurling type modulated with weight …