Titel Deelnemers "Korte inhoud"
"On the projective description of spaces of ultradifferentiable functions of Roumieu type" "Andreas Debrouwere, Bojan Prangoski, Jasson Vindas Diaz" "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 considerably weaker assumptions than in earlier versions of these results."
"Note on vector valued Hardy spaces related to analytic functions having distributional boundary values" "Richard D. Carmichael, Stevan Pilipovic, Jasson Vindas Diaz" "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 $H^{p}(T^{C}, X)$ are also obtained for certain classes of Banach spaces, including reflexive Banach spaces."
"The Fourier transform of thick distributions" "Ricardo Estrada, Jasson Vindas Diaz, Yunyun Yang"
"Infinite order psi DOs : composition with entire functions, new Shubin-Sobolev spaces, and index theorem" "Stevan Pilipovic, Bojan Prangoski, Jasson Vindas Diaz" "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 infinity 8 for which we find the asymptotic behaviour of their eigenvalue counting function. In the second part of the article, we introduce Shubin-Sobolev type spaces by means of f-Gamma(Ap,rho)*(infinity)-elliptic symbols, where f is a function of ultrapolynomial growth and Gamma(Ap,rho)*(infinity) is a class of symbols of infinite order studied in this and our previous papers. We study the regularity properties of these spaces, and show that the pseudo-differential operators under consideration are Fredholm operators on them. Their indices are independent on the order of the Shubin-Sobolev spaces; finally, we show that the index can be expressed via a Fedosov-Hormander integral formula."
"An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions" "Frederik Broucke, Gregory Debruyne, Jasson Vindas Diaz"
"Boundary values, integral transforms, and growth of vector valued Hardy functions" "Richard Carmichael, Stevan Pilipovic, Jasson Vindas Diaz" "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 , all H^p functions, 1 ≤ p ≤ ∞, are shown to equal the Poisson integral of L^p functions, have boundary values in L^p norm on the distinguished boundary R^n + i{0} of the tube T^C , and have pointwise growth properties. For H² functions with values in Hilbert space we show the existence of L² boundary values on the topological boundary R^n + i ∂C of the tube T^C ."
"A multidimensional Tauberian theorem for Laplace transforms of ultradistributions" "Lenny Neyt, Jasson Vindas Diaz"
"Asymptotic boundedness and moment asymptotic expansion in ultradistribution spaces" "Lenny Neyt, Jasson Vindas Diaz"
"Beurling integers with RH and large oscillation" "Frederik Broucke, Gregory Debruyne, Jasson Vindas Diaz"
"Multiresolution expansions and wavelets in Gelfand-Shilov spaces" "Stevan Pilipovic, Dusan Rakic, Nenad Teofanov, Jasson Vindas Diaz" "We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand–Shilov spaces. Important examples of multiresolution analyses for which our results apply arise in particular from Dziubański–Hernández construction of band-limited wavelets with subexponential decay. Our results are twofold. Firstly, we obtain approximation properties of multiresolution expansions of Gelfand–Shilov functions and (ultra)distributions. Secondly, we establish convergence of wavelet series expansions in the same regularity framework."