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

An algorithm for a Pick-Nevanlinna problem where the interpola- tion points coalesce into a finite set of points on the real line is introduced, its connection with certain multipoint Pade approximation problems is discussed, and the results are used to obtain the solutions of an extended Hamburger mo- ment problem. The Pick-Nevanlinna problem is the following: Let {za : a £ A} be a set of distinct points in the open upper half-plane H+ = {z : Imz > 0}, and let {wa : a £ A} be a set of points in C. Find a function F(z) which is analytic in //° such that ImF(z) > 0 for z e //J and F(z) = wa for all a £ A. (A function F(z) which is analytic for z £ HQ+ with ImF(z) > 0 is called a Nevanlinna function.) The problem was solved by Pick (27, 28) in the case that A is finite, by Nevanlinna (15, 16) in the case that A is countable, and by Krein and Rekhtman (14) in the general case. A variant of the problem for finite or countable A arises when all points za coalesce to a single point a , and given values wa at the points are replaced by the Taylor coefficients at a. A problem closely related to this is Caratheodory's coefficient problem (see (2, 3, 33)): Given a finite sequence {y0, ... , ym} or an infinite sequence {yn : n £ N}, find a function F(z) which is analytic in the open unit disc D° = {z : \z\ 0 for z £ D° and F(z) = EZU?*2* + EZm+\okm)zk. or F(z) = Er=o^z?- (For historical remarks on this problem, see (12).) By introducing the linear fractional transformation 7 —► j=£ we can refor- mulate the requirement Re7(z) > 0 to read |7(z)| 0 for z € D°, or a Schur function if |7(z)| < 1 for z E 7J°.) Schur (31) invented an algorithm called the Schur algorithm to deal with this problem. The tech- nique was adapted by Nevanlinna to deal with the Pick-Nevanlinna problem.

A modified Schur algorithm and an extended Hamburger moment problem