Mapping properties of Fourier transforms

DOI10.4171/ZAA/1697arXiv2112.04896MaRDI QIDQ6385200

Publication date: 8 December 2021

Abstract: The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished function spaces on

m a t h b b R^{n}

. The degree of compactness will be measured in terms of related entropy numbers. We are more interested in the interplay of already available ingredients than in generality.

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

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