{"title":"Mumford曲线及其有限商上的热方程和小波","authors":"Patrick Erik Bradley","doi":"10.1007/s00041-023-10046-y","DOIUrl":null,"url":null,"abstract":"Abstract A class of heat operators over non-archimedean local fields acting on $$L_2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -function spaces on holed discs in the local field are developed and seen as being operators previously introduced by Zúñiga-Galindo, and if the underlying trees are regular, they are associated here with certain finite Kronecker product graphs. $$L_2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -spaces and integral operators invariant under the action of a finite group acting on a holed disc are studied, and then applied to Mumford curves. It is found that the spectral gap in families of Mumford curves can become arbitrarily small.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Heat Equations and Wavelets on Mumford Curves and Their Finite Quotients\",\"authors\":\"Patrick Erik Bradley\",\"doi\":\"10.1007/s00041-023-10046-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract A class of heat operators over non-archimedean local fields acting on $$L_2$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -function spaces on holed discs in the local field are developed and seen as being operators previously introduced by Zúñiga-Galindo, and if the underlying trees are regular, they are associated here with certain finite Kronecker product graphs. $$L_2$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -spaces and integral operators invariant under the action of a finite group acting on a holed disc are studied, and then applied to Mumford curves. It is found that the spectral gap in families of Mumford curves can become arbitrarily small.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00041-023-10046-y\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00041-023-10046-y","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Heat Equations and Wavelets on Mumford Curves and Their Finite Quotients
Abstract A class of heat operators over non-archimedean local fields acting on $$L_2$$ L2 -function spaces on holed discs in the local field are developed and seen as being operators previously introduced by Zúñiga-Galindo, and if the underlying trees are regular, they are associated here with certain finite Kronecker product graphs. $$L_2$$ L2 -spaces and integral operators invariant under the action of a finite group acting on a holed disc are studied, and then applied to Mumford curves. It is found that the spectral gap in families of Mumford curves can become arbitrarily small.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.