{"title":"Nonlinear expansions in reproducing kernel Hilbert spaces","authors":"Javad Mashreghi, William Verreault","doi":"10.1007/s43670-023-00069-3","DOIUrl":null,"url":null,"abstract":"We introduce an expansion scheme in reproducing kernel Hilbert spaces, which as a special case covers the celebrated Blaschke unwinding series expansion for analytic functions. The expansion scheme is further generalized to cover Hardy spaces $$H^p$$ , $$1<p<\\infty $$ , viewed as Banach spaces of analytic functions with bounded evaluation functionals. In this setting a dichotomy is more transparent: depending on the multipliers used, the expansion of $$f \\in H^p$$ converges either to f in $$H^p$$ -norm or to its projection onto a model space generated by the corresponding multipliers. Some explicit instances of the general expansion scheme, which are not covered by the previously known methods, are also discussed.","PeriodicalId":74751,"journal":{"name":"Sampling theory, signal processing, and data analysis","volume":"72 4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sampling theory, signal processing, and data analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s43670-023-00069-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce an expansion scheme in reproducing kernel Hilbert spaces, which as a special case covers the celebrated Blaschke unwinding series expansion for analytic functions. The expansion scheme is further generalized to cover Hardy spaces $$H^p$$ , $$1
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