{"title":"单独调和函数的可移动奇异性","authors":"S. Imomkulov, Sultanbay M. Abdikadirov","doi":"10.17516/1997-1397-2021-14-3-369-375","DOIUrl":null,"url":null,"abstract":"Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function u(x, y) in D \\ S to the domain D, when D ⊂ Rn(x) × Rm(y), n,m > 1 and S is a closed subset of the domain D with nowhere dense projections S1 = {x ∈ Rn : (x, y) ∈ S} and S2 = {y ∈ Rm : (x, y) ∈ S}.","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"13 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Removable Singularities of Separately Harmonic Functions\",\"authors\":\"S. Imomkulov, Sultanbay M. Abdikadirov\",\"doi\":\"10.17516/1997-1397-2021-14-3-369-375\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function u(x, y) in D \\\\ S to the domain D, when D ⊂ Rn(x) × Rm(y), n,m > 1 and S is a closed subset of the domain D with nowhere dense projections S1 = {x ∈ Rn : (x, y) ∈ S} and S2 = {y ∈ Rm : (x, y) ∈ S}.\",\"PeriodicalId\":43965,\"journal\":{\"name\":\"Journal of Siberian Federal University-Mathematics & Physics\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Siberian Federal University-Mathematics & Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17516/1997-1397-2021-14-3-369-375\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University-Mathematics & Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2021-14-3-369-375","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Removable Singularities of Separately Harmonic Functions
Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function u(x, y) in D \ S to the domain D, when D ⊂ Rn(x) × Rm(y), n,m > 1 and S is a closed subset of the domain D with nowhere dense projections S1 = {x ∈ Rn : (x, y) ∈ S} and S2 = {y ∈ Rm : (x, y) ∈ S}.
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