English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Complex signed measures of finite total variation are a powerful signal modelin many applications. Restricting to the $d$-dimensional torus, finitelysupported measures allow for exact recovery if the trigonometric moments up tosome order are known. Here, we consider the approximation of general measures,e.g., supported on a curve, by trigonometric polynomials of fixed degree withrespect to the Wasserstein-1 distance. We prove sharp lower bounds for theirbest approximation and (almost) matching upper bounds for effectivelycomputable approximations when the trigonometric moments of the measure areknown. A second class of sum of squares polynomials is shown to interpolate thecharacteristic function on the support of the measure and to converge to zerooutside.

Approximation and Interpolation of Singular Measures by Trigonometric Polynomials