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

The Fourier transform truncated on [-c,c] is usually analyzed when acting onL^2(-1/b,1/b) and its right-singular vectors are the prolate spheroidal wavefunctions. This paper considers the operator acting on the larger spaceL^2(exp(b|.|)) on which it remains injective. We give nonasymptotic upper andlower bounds on the singular values with similar qualitative behavior in m (theindex), b, and c. The lower bounds are used to obtain rates of convergence forstable analytic continuation of possibly nonbandlimited functions whose Fouriertransform belongs to L^2(exp(b|.|)). We also derive bounds on the sup-norm ofthe singular functions. Finally, we propose a numerical method to compute theSVD and apply it to stable analytic continuation when the function is observedwith error on an interval.

Estimates for the SVD of the truncated Fourier transform on L2(exp(b|$\times$|)) and stable analytic continuation