{"title":"算子的复幂","authors":"M. Kostic","doi":"10.2298/PIM0897015K","DOIUrl":null,"url":null,"abstract":"We define the complex powers of a densely defined operator A whose resolvent exists in a suitable region of the complex plane. Generally, this region is strictly contained in an angle and there exists α ∈ (0, ∞ )s uch that the resolvent of A is bounded by O((1 + |λ|) α ) there. We prove that for some particular choices of a fractional number b, the negative of the fractional power (−A) b is the c.i.g. of an analytic semigroup of growth order r> 0.","PeriodicalId":416273,"journal":{"name":"Publications De L'institut Mathematique","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"COMPLEX POWERS OF OPERATORS\",\"authors\":\"M. Kostic\",\"doi\":\"10.2298/PIM0897015K\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define the complex powers of a densely defined operator A whose resolvent exists in a suitable region of the complex plane. Generally, this region is strictly contained in an angle and there exists α ∈ (0, ∞ )s uch that the resolvent of A is bounded by O((1 + |λ|) α ) there. We prove that for some particular choices of a fractional number b, the negative of the fractional power (−A) b is the c.i.g. of an analytic semigroup of growth order r> 0.\",\"PeriodicalId\":416273,\"journal\":{\"name\":\"Publications De L'institut Mathematique\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Publications De L'institut Mathematique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/PIM0897015K\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publications De L'institut Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/PIM0897015K","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
我们定义了一个稠密定义算子a的复幂，它的解存在于复平面的一个合适区域中。一般来说，该区域严格包含在一个角中，且存在α∈(0，∞)s，使得A的解在此以O((1 + |λ|) α)为界。证明了对于分数b的某些特定选择，分数次幂(- a) b的负数是生长阶为r> 0的解析半群的矩阵。
We define the complex powers of a densely defined operator A whose resolvent exists in a suitable region of the complex plane. Generally, this region is strictly contained in an angle and there exists α ∈ (0, ∞ )s uch that the resolvent of A is bounded by O((1 + |λ|) α ) there. We prove that for some particular choices of a fractional number b, the negative of the fractional power (−A) b is the c.i.g. of an analytic semigroup of growth order r> 0.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
