This paper collects a large deal of what is presently known about spherical harmonics on the Heisenberg group and the related functions C~a,B). It contains both new results and new approaches to old results. First, orthogonality properties and generating functions for C~a,B) are discussed. Next a new approach to Koranyi's Kelvin transform on the Heisenberg group is given. After a treatment of Heisenberg harmonics, the Kelvin transform is applied in order to obtain a new proof of Dunkl's ex pansion of the translate of the fundamental solution for L • Finally it y is shown that, if the Dirichlet problem for solvable, then the related functions C (a' B) k L on the Heisenberg ball is y form a complete system.
本文收集了大量目前已知的Heisenberg群上的球谐波及其相关函数C~a,B)。它既包含新结果，也包含对旧结果的新方法。首先，讨论了C~a,B)的正交性和生成函数。然后给出了在Heisenberg群上的Koranyi开尔文变换的一种新方法。在对海森堡谐波进行处理后，应用开尔文变换，得到了L•的基本解平移的Dunkl展开式的新证明，最后证明了如果Dirichlet问题为可解，则海森堡球上的相关函数C (a’B) k L为y构成一个完整的系统。
{"title":"[ERG].","authors":"K. Sato","doi":"10.32388/agclqt","DOIUrl":"https://doi.org/10.32388/agclqt","url":null,"abstract":"This paper collects a large deal of what is presently known about spherical harmonics on the Heisenberg group and the related functions C~a,B). It contains both new results and new approaches to old results. First, orthogonality properties and generating functions for C~a,B) are discussed. Next a new approach to Koranyi's Kelvin transform on the Heisenberg group is given. After a treatment of Heisenberg harmonics, the Kelvin transform is applied in order to obtain a new proof of Dunkl's ex pansion of the translate of the fundamental solution for L • Finally it y is shown that, if the Dirichlet problem for solvable, then the related functions C (a' B) k L on the Heisenberg ball is y form a complete system.","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":"17 1","pages":"1229-33"},"PeriodicalIF":0.0,"publicationDate":"2020-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47933605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Shiraga, N. Matsuo, T. Tsuji, M. Mihara, K. Nasu
{"title":"Risk factors for age-related macular degeneration with choroidal neovascularization","authors":"F. Shiraga, N. Matsuo, T. Tsuji, M. Mihara, K. Nasu","doi":"10.1201/b14548-6","DOIUrl":"https://doi.org/10.1201/b14548-6","url":null,"abstract":"","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":"1046 1","pages":"544-548"},"PeriodicalIF":0.0,"publicationDate":"1989-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77230633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M KISHIMOTO, U YAMANOUCHI, S KAKIMOTO, H UNO, T TAKANO
{"title":"[EFFECTS OF 20 PER CENT MANNITOL ON GLAUCOMATOUS EYES].","authors":"M KISHIMOTO, U YAMANOUCHI, S KAKIMOTO, H UNO, T TAKANO","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":" ","pages":"1255-8"},"PeriodicalIF":0.0,"publicationDate":"1964-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40776617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"[COLOR VISION TEST WITH PSEUDO-ISOCHROMATIC TEST PLATES].","authors":"J SAWA","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":" ","pages":"1207-11"},"PeriodicalIF":0.0,"publicationDate":"1964-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40776610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"[VISIT TO ASIA AND EUROPE (WITH SPECIAL REFERENCE TO THE 2D CONFERENCE OF OPHTHALMOLOGY)].","authors":"K TOZUKA","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":" ","pages":"1273-8"},"PeriodicalIF":0.0,"publicationDate":"1964-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40776619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"[A CASE OF CIRCUMSCRIBED CHORIORETINITIS].","authors":"H ASATANI","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":" ","pages":"1205-6"},"PeriodicalIF":0.0,"publicationDate":"1964-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40779369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"[CONFERENCES ON OPHTHALMOLOGY IN AUSTRALIA AND NEW ZEALAND].","authors":"C SATO","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":" ","pages":"1279-83"},"PeriodicalIF":0.0,"publicationDate":"1964-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40776620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"[STROMAL OVERGROWTH (FIBROBLASTIC INGROWTH) FOLLOWED BY THE EXTRACTION OF A DISLOCATED LENS].","authors":"I TSUKAHARA, S UCHIDA","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":" ","pages":"1213-6"},"PeriodicalIF":0.0,"publicationDate":"1964-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40776611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"[RECENT ADVANCES IN OCULAR THERAPEUTICS WITH SPECIAL REFERENCE TO ENZYMATIC PREPARATIONS].","authors":"T IIZUKA","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":14742,"journal":{"name":"Japanese journal of clinical ophthalmology","volume":" ","pages":"1217-25"},"PeriodicalIF":0.0,"publicationDate":"1964-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40776612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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