{"title":"正则函数空间上微分算子的满射定理","authors":"F. Colombo, A. Damiano, I. Sabadini, D. Struppa","doi":"10.1080/02781070500132679","DOIUrl":null,"url":null,"abstract":"In this article we show that it is possible to construct a Koszul-type complex for maps given by suitable pairwise commuting matrices of polynomials. This result has applications to surjectivity theorems for constant coefficients differential operators of finite and infinite order. In particular, we construct a large class of constant coefficients differential operators which are surjective on the space of regular (or monogenic) functions on open convex sets.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"A surjectivity theorem for differential operators on spaces of regular functions\",\"authors\":\"F. Colombo, A. Damiano, I. Sabadini, D. Struppa\",\"doi\":\"10.1080/02781070500132679\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article we show that it is possible to construct a Koszul-type complex for maps given by suitable pairwise commuting matrices of polynomials. This result has applications to surjectivity theorems for constant coefficients differential operators of finite and infinite order. In particular, we construct a large class of constant coefficients differential operators which are surjective on the space of regular (or monogenic) functions on open convex sets.\",\"PeriodicalId\":272508,\"journal\":{\"name\":\"Complex Variables, Theory and Application: An International Journal\",\"volume\":\"15 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Variables, Theory and Application: An International Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/02781070500132679\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Variables, Theory and Application: An International Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/02781070500132679","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A surjectivity theorem for differential operators on spaces of regular functions
In this article we show that it is possible to construct a Koszul-type complex for maps given by suitable pairwise commuting matrices of polynomials. This result has applications to surjectivity theorems for constant coefficients differential operators of finite and infinite order. In particular, we construct a large class of constant coefficients differential operators which are surjective on the space of regular (or monogenic) functions on open convex sets.
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