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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we find extremal one-sided approximations of exponential typefor a class of truncated and odd functions with a certain exponentialsubordination. These approximations optimize the $L^1(\mathbb{R},|E(x)|^{-2}dx)$-error, where $E$ is an arbitrary Hermite-Biehler entirefunction of bounded type in the upper half-plane. This extends the work of Holtand Vaaler [Duke Math. Journal 83 (1996), 203-247] for the signum function. Wealso provide periodic analogues of these results, finding optimal one-sidedapproximations by trigonometric polynomials of a given degree to a class ofperiodic functions with exponential subordination. These extremal trigonometricpolynomials optimize the $L^1(\mathbb{R}/\mathbb{Z}, d\vartheta)$-error, where$\vartheta$ is an arbitrary nontrivial measure on $\mathbb{R}/\mathbb{Z}$. Theperiodic results extend the work of Li and Vaaler [Indiana Univ. Math. J. 48,No. 1 (1999), 183-236], who considered this problem for the sawtooth functionwith respect to Jacobi measures. Our techniques are based on the theory ofreproducing kernel Hilbert spaces (of entire functions and of polynomials) andon the construction of suitable interpolations with nodes at the zeros ofLaguerre-P\'{o}lya functions.

Extremal problems in de Branges spaces: the case of truncated and odd functions