{"title":"ASSEMBLING RKHS WITH PICK KERNELS AND ASSEMBLING POLYHEDRA IN","authors":"R. Rochberg","doi":"10.4153/s0008414x23000469","DOIUrl":null,"url":null,"abstract":". We study the geometry of Hilbert spaces with complete Pick kernels and the geometry of sets in complex hyperbolic space, taking advantage of the correspondence between the two topics. We focus on questions of assembling Hilbert spaces into larger spaces and of assembling sets into larger sets. Model questions include describing the possible three dimensional subspaces of four dimensional Hilbert spaces with Pick kernels and describing the possible triangular faces of a tetrahedron in CH n . A novel technical tool is a complex analog of the cosine of a vertex angle.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"7 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4153/s0008414x23000469","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
. We study the geometry of Hilbert spaces with complete Pick kernels and the geometry of sets in complex hyperbolic space, taking advantage of the correspondence between the two topics. We focus on questions of assembling Hilbert spaces into larger spaces and of assembling sets into larger sets. Model questions include describing the possible three dimensional subspaces of four dimensional Hilbert spaces with Pick kernels and describing the possible triangular faces of a tetrahedron in CH n . A novel technical tool is a complex analog of the cosine of a vertex angle.
期刊介绍:
The Canadian Journal of Mathematics (CJM) publishes original, high-quality research papers in all branches of mathematics. The Journal is a flagship publication of the Canadian Mathematical Society and has been published continuously since 1949. New research papers are published continuously online and collated into print issues six times each year.
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