Seminar Analysis and Theoretical Physics

Talk on Tuesday, May 14, 2024, at 3 p.m., room c311, main building of the university; Prof. Dr. Dorothee Haroske, Friedrich-Schiller-Universität Jena; Mapping properties of Fourier transform in function spaces, some recent results

Mapping properties of Fourier transforms in function spaces, some recent results


We study continuous and compact mappings generated by the Fourier transform
between distinguished Besov spaces Bsp,p(Rn), 1 ≤ p ≤ ∞, and between Sobolev
spaces Hsp (Rn), 1 < p < ∞. Here we rely mainly on wavelet expansions, duality and
interpolation of corresponding (unweighted) spaces, and (appropriately extended)
Hausdorff-Young inequalities. The degree of compactness will be measured in terms
of entropy numbers and approximation numbers, now using the symbiotic relation-
ship to weighted spaces. We can also characterise the situation when the Fourier
transform acts as a nuclear operator.

This is joint work with Leszek Skrzypczak (Poznań) and Hans Triebel (Jena).