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Microlocal Analysis, Sharp Spectral Asymptotics and Applications V最新文献

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Bethe-Sommerfeld Conjecture in Semiclassical Settings 半经典环境下的贝特-索默菲尔德猜想
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 2019-02-01 DOI: 10.1007/978-3-030-30561-1_36
V. Ivrii
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引用次数: 0
Complete Differentiable Semiclassical Spectral Asymptotics 完全可微半经典谱渐近性
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 2018-09-19 DOI: 10.1007/978-3-030-30561-1_35
V. Ivrii
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引用次数: 0
Complete Semiclassical Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Operators 常算子周期和概周期扰动的完全半经典谱渐近性
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 2018-08-05 DOI: 10.1007/978-3-030-30561-1_34
V. Ivrii
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引用次数: 6
Spectral Asymptotics for Fractional Laplacians 分数阶拉普拉斯算子的谱渐近性
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 2016-03-21 DOI: 10.1007/978-3-030-30561-1_30
V. Ivrii
{"title":"Spectral Asymptotics for Fractional Laplacians","authors":"V. Ivrii","doi":"10.1007/978-3-030-30561-1_30","DOIUrl":"https://doi.org/10.1007/978-3-030-30561-1_30","url":null,"abstract":"","PeriodicalId":310753,"journal":{"name":"Microlocal Analysis, Sharp Spectral Asymptotics and Applications V","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125198686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Spectral Asymptotics for the Semiclassical Dirichlet to Neumann Operator 半经典Dirichlet - Neumann算子的谱渐近性
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 2015-05-19 DOI: 10.4171/JST/180
Andrew Hassell, V. Ivrii
{"title":"Spectral Asymptotics for the Semiclassical Dirichlet to Neumann Operator","authors":"Andrew Hassell, V. Ivrii","doi":"10.4171/JST/180","DOIUrl":"https://doi.org/10.4171/JST/180","url":null,"abstract":"Let $M$ be a compact Riemannian manifold with smooth boundary, and let $R(lambda)$ be the Dirichlet-to-Neumann operator at frequency $lambda$. We obtain a leading asymptotic for the spectral counting function for $lambda^{-1}R(lambda)$ in an interval $[a_1, a_2)$ as $lambda to infty$, under the assumption that the measure of periodic billiards on $T^*M$ is zero. The asymptotic takes the form begin{equation*} N(lambda; a_1,a_2) = bigl(kappa(a_2)-kappa(a_1)bigr)mathsf{vol}'(partial M) lambda^{d-1}+o(lambda^{d-1}), end{equation*} where $kappa(a)$ is given explicitly by begin{equation*} kappa(a) = frac{omega_{d-1}}{(2pi)^{d-1}} biggl( -frac{1}{2pi} int_{-1}^1 (1 - eta^2)^{(d-1)/2} frac{a}{a^2 + eta^2} , deta - frac{1}{4} + H(a) (1+a^2)^{(d-1)/2} biggr) end{equation*} with the Heavyside function $H(a)$.","PeriodicalId":310753,"journal":{"name":"Microlocal Analysis, Sharp Spectral Asymptotics and Applications V","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125184580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
The Case of Self-Generated Magnetic Field 自生磁场的情况
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 1900-01-01 DOI: 10.1007/978-3-030-30561-1_27
V. Ivrii
{"title":"The Case of Self-Generated Magnetic Field","authors":"V. Ivrii","doi":"10.1007/978-3-030-30561-1_27","DOIUrl":"https://doi.org/10.1007/978-3-030-30561-1_27","url":null,"abstract":"","PeriodicalId":310753,"journal":{"name":"Microlocal Analysis, Sharp Spectral Asymptotics and Applications V","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128027205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral Asymptotics for Dirichlet to Neumann Operator in the Domains with Edges 有边域上Dirichlet - Neumann算子的谱渐近性
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 1900-01-01 DOI: 10.1007/978-3-030-30561-1_31
V. Ivrii
{"title":"Spectral Asymptotics for Dirichlet to Neumann Operator in the Domains with Edges","authors":"V. Ivrii","doi":"10.1007/978-3-030-30561-1_31","DOIUrl":"https://doi.org/10.1007/978-3-030-30561-1_31","url":null,"abstract":"","PeriodicalId":310753,"journal":{"name":"Microlocal Analysis, Sharp Spectral Asymptotics and Applications V","volume":"53 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116534467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
No Magnetic Field Case 无磁场情况
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 1900-01-01 DOI: 10.1007/978-3-030-30561-1_25
V. Ivrii
{"title":"No Magnetic Field Case","authors":"V. Ivrii","doi":"10.1007/978-3-030-30561-1_25","DOIUrl":"https://doi.org/10.1007/978-3-030-30561-1_25","url":null,"abstract":"","PeriodicalId":310753,"journal":{"name":"Microlocal Analysis, Sharp Spectral Asymptotics and Applications V","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131322480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Case of Combined Magnetic Field 结合磁场的情况
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 1900-01-01 DOI: 10.1007/978-3-030-30561-1_28
V. Ivrii
{"title":"The Case of Combined Magnetic Field","authors":"V. Ivrii","doi":"10.1007/978-3-030-30561-1_28","DOIUrl":"https://doi.org/10.1007/978-3-030-30561-1_28","url":null,"abstract":"","PeriodicalId":310753,"journal":{"name":"Microlocal Analysis, Sharp Spectral Asymptotics and Applications V","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129663875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Case of External Magnetic Field 外磁场的情况
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V Pub Date : 1900-01-01 DOI: 10.1007/978-3-030-30561-1_26
V. Ivrii
{"title":"The Case of External Magnetic Field","authors":"V. Ivrii","doi":"10.1007/978-3-030-30561-1_26","DOIUrl":"https://doi.org/10.1007/978-3-030-30561-1_26","url":null,"abstract":"","PeriodicalId":310753,"journal":{"name":"Microlocal Analysis, Sharp Spectral Asymptotics and Applications V","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132860610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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