{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T06:21:48Z","timestamp":1764829308033,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T00:00:00Z","timestamp":1753574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12371098","JYT202102"],"award-info":[{"award-number":["12371098","JYT202102"]}]},{"name":"Fundamental Research Funds for Universities in Hebei Province","award":["12371098","JYT202102"],"award-info":[{"award-number":["12371098","JYT202102"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let \u039b\u2286Rd be a discrete uniformly separated subset. In the unweighted case and p=2, Landau obtained the necessary conditions for sampling and interpolation of functions in Paley\u2013Wiener space in terms of the upper and lower uniform densities of \u039b. In this paper, we generalize the above results to the weighted case, and give some necessary density conditions for Lp weighted sampling and interpolating sets for all 0&lt;p&lt;\u221e.<\/jats:p>","DOI":"10.3390\/axioms14080584","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T09:53:02Z","timestamp":1753696382000},"page":"584","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Necessary Density Conditions for Sampling and Interpolation of Certain Entire Functions with Doubling Weights"],"prefix":"10.3390","volume":"14","author":[{"given":"Xuebo","family":"Zhai","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6212-5760","authenticated-orcid":false,"given":"Kai","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Langfang Normal University, Langfang 065000, China"}]},{"given":"Heping","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Seip, K. 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