{"title":"邓克尔多谐函数的均值特征","authors":"G. Łysik","doi":"10.1007/s10474-024-01398-y","DOIUrl":null,"url":null,"abstract":"<div><p>We give characterizations of the Dunkl polyharmonic functions,\ni.e., solutions to the iteration of the Dunkl-Laplace operator <span>\\(\\Delta_\\kappa\\)</span> which\nis a differential-reflection operator associated with a Coxeter–Weil group <span>\\(W\\)</span> generated\nby a finite set of reflections and an invariant multiplicity function <span>\\(\\kappa\\)</span>, in\nterms of integral means over Euclidean balls and spheres.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"172 1","pages":"119 - 130"},"PeriodicalIF":0.6000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mean value characterizations of the Dunkl polyharmonic functions\",\"authors\":\"G. Łysik\",\"doi\":\"10.1007/s10474-024-01398-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We give characterizations of the Dunkl polyharmonic functions,\\ni.e., solutions to the iteration of the Dunkl-Laplace operator <span>\\\\(\\\\Delta_\\\\kappa\\\\)</span> which\\nis a differential-reflection operator associated with a Coxeter–Weil group <span>\\\\(W\\\\)</span> generated\\nby a finite set of reflections and an invariant multiplicity function <span>\\\\(\\\\kappa\\\\)</span>, in\\nterms of integral means over Euclidean balls and spheres.</p></div>\",\"PeriodicalId\":50894,\"journal\":{\"name\":\"Acta Mathematica Hungarica\",\"volume\":\"172 1\",\"pages\":\"119 - 130\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10474-024-01398-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01398-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Mean value characterizations of the Dunkl polyharmonic functions
We give characterizations of the Dunkl polyharmonic functions,
i.e., solutions to the iteration of the Dunkl-Laplace operator \(\Delta_\kappa\) which
is a differential-reflection operator associated with a Coxeter–Weil group \(W\) generated
by a finite set of reflections and an invariant multiplicity function \(\kappa\), in
terms of integral means over Euclidean balls and spheres.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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