Publicaties
Besov regularity in non-linear generalized functions Universiteit Gent
The pointwise behavior of Riemann’s function Universiteit Gent
We present a new and simple method for the determination of the pointwise Hölder exponent of Riemann’s function $\sum_{n=1}^{\infty} \sin(\pi n^2 x)/n^2$ at every point of the real line. In contrast to earlier approaches, where wavelet analysis and the theta modular group were needed for the analysis of irrational points, our method is direct and elementary, being only based on the following tools from number theory and complex analysis: the ...
Quasianalytic functionals and ultradistributions as boundary values of harmonic functions Universiteit Gent
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to Hörmander’s support theorem for quasianalytic functionals. Our main technical tool is a description of ultradifferentiable functions by almost harmonic functions, a concept that we introduce in this article. We work in the setting of ultradifferentiable ...
Note on vector valued Hardy spaces related to analytic functions having distributional boundary values Universiteit Gent
Analytic functions defined on a tube domain $T^{C}\subset \mathbb{C}^{n}$ and taking values in a Banach space $X$ which are known to have $X$-valued distributional boundary values are shown to be in the Hardy space $H^{p}(T^{C},X)$ if the boundary value is in the vector valued Lebesgue space $L^{p}(\mathbb{R}^{n},X)$, where $1\leq p \leq \infty$ and $C$ is a regular open convex cone. Poisson integral transform representations of elements of ...
On the projective description of spaces of ultradifferentiable functions of Roumieu type Universiteit Gent
We provide a projective description of the space E{M}(Ω) of ultradifferentiable functions of Roumieu type, where Ω is an arbitrary open set in Rd and M is a weight matrix satisfying the analogue of Komatsu’s condition (M.2)′. In particular, we obtain in a unified way projective descriptions of ultradifferentiable classes defined via a single weight sequence (Denjoy-Carleman approach) and via a weight function (Braun-Meise-Taylor approach) under ...
The Fourier transform of thick distributions Universiteit Gent
An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions Universiteit Gent
Boundary values, integral transforms, and growth of vector valued Hardy functions Universiteit Gent
Banach space valued Hardy functions H^p, 0 < p ≤ ∞, are defined with the functions having domain in tubes T^C = R^n + iC ⊂ C^n; H² functions with values in Hilbert space are characterized as Fourier-Laplace transforms of functions which satisfy a certain norm growth property. These H² functions are shown to equal a Cauchy integral when the base C of the tube T^C is specialized. For certain Banach spaces and certain bases C of the tube T^C , ...
Infinite order psi DOs : composition with entire functions, new Shubin-Sobolev spaces, and index theorem Universiteit Gent
We study global regularity and spectral properties of power series of the Weyl quantisation a(w), where a(x, xi) is a classical elliptic Shubin polynomial. For a suitable entire function P, we associate two natural infinite order operators to a(w), P(a(w)) and (P. a)(w), and prove that these operators and their lower order perturbations are globally Gelfand-Shilov regular. They have spectra consisting of real isolated eigenvalues diverging to ...