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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

For a function g(w) analytic and univalent in {w:1<|w|<\infty} with a simplepole at \infty and a continuous extension to {w:|w|\geq 1}, we consider theFaber polynomials F_n(z), n=0,1,2,..., associated to g(w) via their generatingfunction g'(w)/(g(w)-z)=\sum_{n=0}^\infty F_n(z)w^{-(n+1)}. Assuming that g(w)maps the unit circle T onto a piecewise analytic curve L whose exterior domainhas no outward-pointing cusps, and under an additional assumption concerningthe "Lehman expansion" of g(w) about those points of T mapped onto corners ofL, we obtain asymptotic formulas for F_n(z) that yield fine results on thelocation, limiting distribution and accumulation points of the zeros of theFaber polynomials. The asymptotic formulas are shown to hold uniformly and theexact rate of decay of the error terms involved is provided.

On the asymptotic behavior of Faber polynomials for domains with piecewise analytic boundary