{"title":"Global Existence of Large Data Weak Solutions for a Simplified Compressible Oldroyd--B Model Without Stress Diffusion","authors":"global sci","doi":"10.4208/ata.oa-su3","DOIUrl":"https://doi.org/10.4208/ata.oa-su3","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"1 1","pages":"348-372"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88670884","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}
{"title":"Boundary Values of Generalized Harmonic Functions Associated with the Rank-One Dunkl Operator","authors":"global sci","doi":"10.4208/ata.oa-su11","DOIUrl":"https://doi.org/10.4208/ata.oa-su11","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"3 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82844426","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}
{"title":"Lipschitz Invariance of Critical Exponents on Besov Spaces","authors":"global sci","doi":"10.4208/ata.oa-su5","DOIUrl":"https://doi.org/10.4208/ata.oa-su5","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"47 1","pages":"457-467"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81592940","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}
{"title":"A Survey on Some Anisotropic Hardy-Type Function Spaces","authors":"global sci","doi":"10.4208/ata.oa-su10","DOIUrl":"https://doi.org/10.4208/ata.oa-su10","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"47 1","pages":"373-456"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89803262","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}
The eigenvalues of a differential operator on a Hilbert-Pólya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann ζ-function. Moreover, their corresponding multiplicities are the same.
{"title":"Eigenvalues of a Differential Operator and Zeros of the Riemann $zeta$-Function","authors":"L. Ge","doi":"10.4208/ata.oa-su1","DOIUrl":"https://doi.org/10.4208/ata.oa-su1","url":null,"abstract":"The eigenvalues of a differential operator on a Hilbert-Pólya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann ζ-function. Moreover, their corresponding multiplicities are the same.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"132 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75406985","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}
Pub Date : 2020-04-23DOI: 10.4208/ata.oa-2021-0051
H. Aimar, Juan Comesatti, I. G'omez, Luis Nowak
In this note we show that the general theory of vector valued singular integral operators of Calderon-Zygmund defined on general metric measure spaces, can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian. In doing so, we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.
{"title":"Partial Derivatives, Singular Integrals and Sobolev Spaces in Dyadic Settings","authors":"H. Aimar, Juan Comesatti, I. G'omez, Luis Nowak","doi":"10.4208/ata.oa-2021-0051","DOIUrl":"https://doi.org/10.4208/ata.oa-2021-0051","url":null,"abstract":"In this note we show that the general theory of vector valued singular integral operators of Calderon-Zygmund defined on general metric measure spaces, can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian. In doing so, we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77405736","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}
Pub Date : 2020-03-22DOI: 10.4208/ata.OA-2020-0047
Christopher Felder
For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.
{"title":"General Optimal Polynomial Approximants, Stabilization, and Projections of Unity","authors":"Christopher Felder","doi":"10.4208/ata.OA-2020-0047","DOIUrl":"https://doi.org/10.4208/ata.OA-2020-0047","url":null,"abstract":"For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88890897","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}
Pub Date : 2020-01-07DOI: 10.4208/ata.oa-2020-0037
Ruggero Freddi
In this paper we consider the Dirichlet problem begin{equation} label{iniz} begin{cases} -Delta u = rho^2 (e^{u} - e^{-u}) & text{ in } Omega u=0 & text{ on } partial Omega, end{cases} end{equation} where $rho$ is a small parameter and $Omega$ is a $C^2$ bounded domain in $mathbb{R}^2$. [1] proves the existence of a $m$-point blow-up solution $u_rho$ jointly with its asymptotic behaviour. we compute the Morse index of $u_rho$ in terms of the Morse index of the associated Hamilton function of this problem. In addition, we give an asymptotic estimate for the first $4m$ eigenvalues and eigenfunctions.
本文考虑了Dirichlet问题begin{equation} label{iniz} begin{cases} -Delta u = rho^2 (e^{u} - e^{-u}) & text{ in } Omega u=0 & text{ on } partial Omega, end{cases} end{equation}，其中$rho$是一个小参数，$Omega$是$mathbb{R}^2$中的一个$C^2$有界域。[1]证明了一个$m$ -点爆破解$u_rho$的存在性及其渐近性。我们根据这个问题的相关汉密尔顿函数的摩尔斯指数来计算$u_rho$的摩尔斯指数。此外，我们给出了第一个$4m$特征值和特征函数的渐近估计。
{"title":"Morse Index of Multiple Blow-Up Solutions to the Two-Dimensional Sinh-Poisson Equation","authors":"Ruggero Freddi","doi":"10.4208/ata.oa-2020-0037","DOIUrl":"https://doi.org/10.4208/ata.oa-2020-0037","url":null,"abstract":"In this paper we consider the Dirichlet problem begin{equation} label{iniz} begin{cases} -Delta u = rho^2 (e^{u} - e^{-u}) & text{ in } Omega u=0 & text{ on } partial Omega, end{cases} end{equation} where $rho$ is a small parameter and $Omega$ is a $C^2$ bounded domain in $mathbb{R}^2$. [1] proves the existence of a $m$-point blow-up solution $u_rho$ jointly with its asymptotic behaviour. we compute the Morse index of $u_rho$ in terms of the Morse index of the associated Hamilton function of this problem. In addition, we give an asymptotic estimate for the first $4m$ eigenvalues and eigenfunctions.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"165 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73579106","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}
Pub Date : 2019-06-18DOI: 10.4208/ata.oa-2020-0036
M. I. Qureshi, S. Jabee, Dilshad Ahamad
The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument, when one numerator parameter and one denominator parameter are negative integers. Further, using our truncated summation theorems, we obtain the Mellin transforms of the product of exponential function and Goursat's truncated hypergeometric function.
{"title":"Some Summation Theorems for Truncated Clausen Series and Applications","authors":"M. I. Qureshi, S. Jabee, Dilshad Ahamad","doi":"10.4208/ata.oa-2020-0036","DOIUrl":"https://doi.org/10.4208/ata.oa-2020-0036","url":null,"abstract":"The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument, when one numerator parameter and one denominator parameter are negative integers. Further, using our truncated summation theorems, we obtain the Mellin transforms of the product of exponential function and Goursat's truncated hypergeometric function.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"3 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84240875","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}
We consider the Monge-Ampere equation $det(D^2u)=f$ in $mathbb{R}^n$, where $f$ is a positive bounded periodic function. We prove that $u$ must be the sum of a quadratic polynomial and a periodic function. For $fequiv 1$, this is the classic result by Jorgens, Calabi and Pogorelov. For $fin C^alpha$, this was proved by Caffarelli and the first named author.
{"title":"Monge-Ampère Equation with Bounded Periodic Data","authors":"Yanyan Li, Siyuan Lu","doi":"10.4208/ata.oa-0022","DOIUrl":"https://doi.org/10.4208/ata.oa-0022","url":null,"abstract":"We consider the Monge-Ampere equation $det(D^2u)=f$ in $mathbb{R}^n$, where $f$ is a positive bounded periodic function. We prove that $u$ must be the sum of a quadratic polynomial and a periodic function. For $fequiv 1$, this is the classic result by Jorgens, Calabi and Pogorelov. For $fin C^alpha$, this was proved by Caffarelli and the first named author.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"84 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83875253","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}
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