{"title":"黎曼曲面上沿测地线的傅里叶展开","authors":"A. Deitmar","doi":"10.2478/s11533-013-0366-x","DOIUrl":null,"url":null,"abstract":"For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"85 1","pages":"559-573"},"PeriodicalIF":0.0000,"publicationDate":"2014-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Fourier expansion along geodesics on Riemann surfaces\",\"authors\":\"A. Deitmar\",\"doi\":\"10.2478/s11533-013-0366-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.\",\"PeriodicalId\":50988,\"journal\":{\"name\":\"Central European Journal of Mathematics\",\"volume\":\"85 1\",\"pages\":\"559-573\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Central European Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/s11533-013-0366-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Central European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/s11533-013-0366-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fourier expansion along geodesics on Riemann surfaces
For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.
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