Concept
Espace de Schwartz
Publications associées (23)
Explicit representations for Banach subspaces of Lizorkin distributions
Michaël Unser, Sebastian Jonas Neumayer
The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...
WORLD SCIENTIFIC PUBL CO PTE LTD2023The inductive bias of deep learning: Connecting weights and functions
Years of a fierce competition have naturally selected the fittest deep learning algorithms. Yet, although these models work well in practice, we still lack a proper characterization of why they do so. This poses serious questions about the robustness, trus ...
EPFL2023Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains
Bernard Kapidani, Rafael Vazquez Hernandez
When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mortaring has been shown to be advantageous. This contribu ...
ELSEVIER SCIENCE SA2022Fourier uniqueness and interpolation in Euclidean space
We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...
EPFL2022Perturbed Fourier uniqueness and interpolation results in higher dimensions
Joao Pedro Gonçalves Ramos, Martin Peter Stoller
We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2022Single and multiple recurrence along non-polynomial sequences
We establish new recurrence and multiple recurrence results for a rather large family of non-polynomial functions which contains tempered functions and (non-polynomial) functions from a Hardy field with polynomial growth. In particular, we show that, somew ...
2020