{"title":"无穷指标p可和函数空间中的Riemann边值问题","authors":"S. Aghekyan","doi":"10.54503/0002-3043-2022.57.6-3-11","DOIUrl":null,"url":null,"abstract":"Abstract. The paper considers the Riemann boundary value problem in the half-plane in the space Lp(ρ), where weight function ρ(x) has infinite number of zeros. A necessary and sufficient condition is obtained for the normal solvability and Noetherianness of the considered problem. If the problem is solvable, solutions are represented in an explicit form.","PeriodicalId":388049,"journal":{"name":"Proceedings of NAS RA. Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a Riemann boundary value problem in the space of p-summable functions with infinite index\",\"authors\":\"S. Aghekyan\",\"doi\":\"10.54503/0002-3043-2022.57.6-3-11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. The paper considers the Riemann boundary value problem in the half-plane in the space Lp(ρ), where weight function ρ(x) has infinite number of zeros. A necessary and sufficient condition is obtained for the normal solvability and Noetherianness of the considered problem. If the problem is solvable, solutions are represented in an explicit form.\",\"PeriodicalId\":388049,\"journal\":{\"name\":\"Proceedings of NAS RA. Mathematics\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of NAS RA. Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.54503/0002-3043-2022.57.6-3-11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of NAS RA. Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54503/0002-3043-2022.57.6-3-11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On a Riemann boundary value problem in the space of p-summable functions with infinite index
Abstract. The paper considers the Riemann boundary value problem in the half-plane in the space Lp(ρ), where weight function ρ(x) has infinite number of zeros. A necessary and sufficient condition is obtained for the normal solvability and Noetherianness of the considered problem. If the problem is solvable, solutions are represented in an explicit form.