{"title":"调和函数的一个性质","authors":"Josip Globevnik , Walter Rudin","doi":"10.1016/S1385-7258(88)80020-9","DOIUrl":null,"url":null,"abstract":"<div><p>Gauss' mean value characterization of harmonic functions involves circles (or spheres) centered at every point of the domain of the function. The present paper gives a criterion of this type which involves only one point of the domain; to make up for this, circles or spheres are replaced by a larger family of convex curves or surfaces which surround this point.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 419-426"},"PeriodicalIF":0.0000,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80020-9","citationCount":"10","resultStr":"{\"title\":\"A characterization of harmonic functions\",\"authors\":\"Josip Globevnik , Walter Rudin\",\"doi\":\"10.1016/S1385-7258(88)80020-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Gauss' mean value characterization of harmonic functions involves circles (or spheres) centered at every point of the domain of the function. The present paper gives a criterion of this type which involves only one point of the domain; to make up for this, circles or spheres are replaced by a larger family of convex curves or surfaces which surround this point.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"91 4\",\"pages\":\"Pages 419-426\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80020-9\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1385725888800209\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725888800209","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Gauss' mean value characterization of harmonic functions involves circles (or spheres) centered at every point of the domain of the function. The present paper gives a criterion of this type which involves only one point of the domain; to make up for this, circles or spheres are replaced by a larger family of convex curves or surfaces which surround this point.
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