{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:30:28Z","timestamp":1740137428648,"version":"3.37.3"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2652018054"],"award-info":[{"award-number":["2652018054"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p> We study the orthogonal rational functions with a given sequence of poles on the half plane. We give the weak-star convergence results for the rational measures which relate to the Poisson kernel and reproducing kernel. Those rational measures represent the same inner product as the normalized Nevanlinna measure in [Formula: see text]. Moreover, we consider the convergence properties of the interpolants which interpolate the Carath\u00e9odory function [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219691320500320","type":"journal-article","created":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T04:56:50Z","timestamp":1590382610000},"page":"2050032","source":"Crossref","is-referenced-by-count":1,"title":["The convergence properties of orthogonal rational functions on the extended real line and analytic on the upper half plane"],"prefix":"10.1142","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9169-1323","authenticated-orcid":false,"given":"Xu","family":"Xu","sequence":"first","affiliation":[{"name":"School of Science, China University of Geosciences, Beijing 100083, P. R. China"}]},{"given":"Xiaoqiang","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering and Information, Northeast Agricultural University, Harbin 150030, P. R. China"}]},{"given":"Laiyi","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Renmin University of China, Beijing 100872, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2020,5,23]]},"reference":[{"doi-asserted-by":"publisher","key":"S0219691320500320BIB001","DOI":"10.1017\/CBO9780511530050"},{"key":"S0219691320500320BIB002","first-page":"1278","volume":"147","author":"D\u017erba\u0161jan M. M.","year":"1962","journal-title":"Dokl. Akad. Nauk SSSR"},{"volume-title":"Orthogonal Polynomials","year":"1971","author":"Freud G.","key":"S0219691320500320BIB003"},{"volume-title":"Bounded Analytic Functions","year":"1981","author":"Garnett J. 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