非阿基米德值拟不变量在无穷测度下递减

IF 1 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2004-05-12 DOI:10.1155/IJMMS.2005.3799

S. Ludkovsky

{"title":"非阿基米德值拟不变量在无穷测度下递减","authors":"S. Ludkovsky","doi":"10.1155/IJMMS.2005.3799","DOIUrl":null,"url":null,"abstract":"Measures with values in non-Archimedean fields, which are quasi-invariant and descending at infinity on topological vector spaces over non-Archimedean fields, are studied in this paper. Moreover, their characteristic functionals are considered. In particular, measures having convolution properties like classical Gaussian measures are investigated in the paper. Applications of such measures to pseudodifferential operators and stochastic processes are considered. Nevertheless, it is proved that there does not exist the complete non-Archimedean analog of Gaussian measures. Theorems about either equivalence or orthogonality of measures from the considered class are proved. In addition, a pseudodifferentiability of such measures is investigated.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2004-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/IJMMS.2005.3799","citationCount":"25","resultStr":"{\"title\":\"Non-archimedean valued quasi-invariant descending at infinity measures\",\"authors\":\"S. Ludkovsky\",\"doi\":\"10.1155/IJMMS.2005.3799\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Measures with values in non-Archimedean fields, which are quasi-invariant and descending at infinity on topological vector spaces over non-Archimedean fields, are studied in this paper. Moreover, their characteristic functionals are considered. In particular, measures having convolution properties like classical Gaussian measures are investigated in the paper. Applications of such measures to pseudodifferential operators and stochastic processes are considered. Nevertheless, it is proved that there does not exist the complete non-Archimedean analog of Gaussian measures. Theorems about either equivalence or orthogonality of measures from the considered class are proved. In addition, a pseudodifferentiability of such measures is investigated.\",\"PeriodicalId\":39893,\"journal\":{\"name\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2004-05-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/IJMMS.2005.3799\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/IJMMS.2005.3799\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/IJMMS.2005.3799","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 25

摘要

研究了非阿基米德域上具有值的拓扑向量空间上的拟不变且在无穷远处递减的测度。此外，还考虑了它们的特征泛函。特别地，本文研究了像经典高斯测度那样具有卷积性质的测度。讨论了这些测度在伪微分算子和随机过程中的应用。然而，证明了不存在高斯测度的完全非阿基米德类似。证明了该类测度的等价性定理和正交性定理。此外，还研究了这类测度的伪可微性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Non-archimedean valued quasi-invariant descending at infinity measures

Measures with values in non-Archimedean fields, which are quasi-invariant and descending at infinity on topological vector spaces over non-Archimedean fields, are studied in this paper. Moreover, their characteristic functionals are considered. In particular, measures having convolution properties like classical Gaussian measures are investigated in the paper. Applications of such measures to pseudodifferential operators and stochastic processes are considered. Nevertheless, it is proved that there does not exist the complete non-Archimedean analog of Gaussian measures. Theorems about either equivalence or orthogonality of measures from the considered class are proved. In addition, a pseudodifferentiability of such measures is investigated.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.