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Corona Theorem.
arXiv: Functional Analysis Pub Date : 2021-06-29 DOI: 10.1016/s0079-8169(08)62676-8
M. Kosiek, K. Rudol
{"title":"Corona Theorem.","authors":"M. Kosiek, K. Rudol","doi":"10.1016/s0079-8169(08)62676-8","DOIUrl":"https://doi.org/10.1016/s0079-8169(08)62676-8","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86358517","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 Tomas–Stein inequality under the effect of symmetries 对称作用下的托马斯-斯坦不等式
arXiv: Functional Analysis Pub Date : 2021-06-15 DOI: 10.5445/IR/1000134152
Rainer Mandel, D. O. Silva
{"title":"The Tomas–Stein inequality under the effect of symmetries","authors":"Rainer Mandel, D. O. Silva","doi":"10.5445/IR/1000134152","DOIUrl":"https://doi.org/10.5445/IR/1000134152","url":null,"abstract":"We prove new Fourier restriction estimates to the unit sphere $mathbb{S}^{d-1}$ on the class of $O(d−k) times O(k)$-symmetric functions, for every $d ge 4$ and $2 le k le d-2$. As an application, we establish the existence of maximizers for the endpoint Tomas–Stein inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp in the Tomas–Stein regime.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73747058","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: 1
Uniqueness of unconditional basis of $ell _{2}oplus mathcal {T}^{(2)}$ $ well _{2}oplus mathcal {T}^{(2)}$的无条件基的唯一性
arXiv: Functional Analysis Pub Date : 2020-12-12 DOI: 10.1090/PROC/15670
F. Albiac, J. L. Ansorena
{"title":"Uniqueness of unconditional basis of $ell _{2}oplus mathcal {T}^{(2)}$","authors":"F. Albiac, J. L. Ansorena","doi":"10.1090/PROC/15670","DOIUrl":"https://doi.org/10.1090/PROC/15670","url":null,"abstract":"We provide a new extension of Pitt's theorem for compact operators between quasi-Banach lattices, which permits to describe unconditional bases of finite direct sums of Banach spaces $mathbb{X}_{1}oplusdotsoplusmathbb{X}_{n}$ as direct sums of unconditional bases of its summands. The general splitting principle we obtain yields, in particular, that if each $mathbb{X}_{i}$ has a unique unconditional basis (up to equivalence and permutation), then $mathbb{X}_{1}oplus cdotsoplusmathbb{X}_{n}$ has a unique unconditional basis too. Among the novel applications of our techniques to the structure of Banach and quasi-Banach spaces we have that the space $ell_2oplus mathcal{T}^{(2)}$ has a unique unconditional basis.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86670029","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
Stability of solutions to some abstract evolution equations with delay 一类具有时滞的抽象演化方程解的稳定性
arXiv: Functional Analysis Pub Date : 2020-12-11 DOI: 10.47443/cm.2021.0004
N. S. Hoang, A. Ramm
{"title":"Stability of solutions to some abstract evolution equations with delay","authors":"N. S. Hoang, A. Ramm","doi":"10.47443/cm.2021.0004","DOIUrl":"https://doi.org/10.47443/cm.2021.0004","url":null,"abstract":"The global existence and stability of the solution to the delay differential equation (*)$dot{u} = A(t)u + G(t,u(t-tau)) + f(t)$, $tge 0$, $u(t) = v(t)$, $-tau le tle 0$, are studied. Here $A(t):mathcal{H}to mathcal{H}$ is a closed, densely defined, linear operator in a Hilbert space $mathcal{H}$ and $G(t,u)$ is a nonlinear operator in $mathcal{H}$ continuous with respect to $u$ and $t$. We assume that the spectrum of $A(t)$ lies in the half-plane $Re lambda le gamma(t)$, where $gamma(t)$ is not necessarily negative and $|G(t,u)| le alpha(t)|u|^p$, $p>1$, $tge 0$. Sufficient conditions for the solution to the equation to exist globally, to be bounded and to converge to zero as $t$ tends to $infty$, under the non-classical assumption that $gamma(t)$ can take positive values, are proposed and justified.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85405567","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
Some more twisted Hilbert spaces 更多扭曲的希尔伯特空间
arXiv: Functional Analysis Pub Date : 2020-12-11 DOI: 10.5186/aasfm.2021.4653
Daniel Morales, J. Su'arez
{"title":"Some more twisted Hilbert spaces","authors":"Daniel Morales, J. Su'arez","doi":"10.5186/aasfm.2021.4653","DOIUrl":"https://doi.org/10.5186/aasfm.2021.4653","url":null,"abstract":"We provide three new examples of twisted Hilbert spaces by considering properties that are \"close\" to Hilbert. We denote them $Z(mathcal J)$, $Z(mathcal S^2)$ and $Z(mathcal T_s^2)$. The first space is asymptotically Hilbertian but not weak Hilbert. On the opposite side, $Z(mathcal S^2)$ and $Z(mathcal T_s^2)$ are not asymptotically Hilbertian. Moreover, the space $Z(mathcal T_s^2)$ is a HAPpy space and the technique to prove it gives a \"twisted\" version of a theorem of Johnson and Szankowski (Ann. of Math. 176:1987--2001, 2012). This is, we can construct a nontrivial twisted Hilbert space such that the isomorphism constant from its $n$-dimensional subspaces to $ell_2^n$ grows to infinity as slowly as we wish when $nto infty$.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87661192","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
Besov-Hankel norms in terms of the continuous Bessel wavelet transform 用连续贝塞尔小波变换表示的贝索夫-汉克尔范数
arXiv: Functional Analysis Pub Date : 2020-12-02 DOI: 10.22541/au.163257138.88871318/v1
Ashish Pathak, Dileep Kumar
{"title":"Besov-Hankel norms in terms of the continuous Bessel wavelet transform","authors":"Ashish Pathak, Dileep Kumar","doi":"10.22541/au.163257138.88871318/v1","DOIUrl":"https://doi.org/10.22541/au.163257138.88871318/v1","url":null,"abstract":"Using the theory of continuous Bessel wavelet transform in $L^2\u0000(mathbb{R})$-spaces, we established the Parseval and\u0000inversion formulas for the\u0000$L^{p,sigma}(mathbb{R}^+)$-\u0000spaces. We investigate continuity and boundedness properties of Bessel\u0000wavelet transform in Besov-Hankel spaces. Our main results: are the\u0000characterization of Besov-Hankel spaces by using continuous Bessel\u0000wavelet coefficient.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81093276","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: 1
Integral $K$-Operator Frames for $End_{mathcal{A}}^{ast}(mathcal{H})$ 整数$K$- $End_{mathcal{A}}^{ast}(mathcal{H})$的运算符框架
arXiv: Functional Analysis Pub Date : 2020-11-30 DOI: 10.22130/SCMA.2021.140176.874
H. Labrigui, S. Kabbaj
{"title":"Integral $K$-Operator Frames for $End_{mathcal{A}}^{ast}(mathcal{H})$","authors":"H. Labrigui, S. Kabbaj","doi":"10.22130/SCMA.2021.140176.874","DOIUrl":"https://doi.org/10.22130/SCMA.2021.140176.874","url":null,"abstract":"In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from Hilbert $C^{ast}$-modules $mathcal{H}$ to it self noted $End_{mathcal{A}}^{ast}(mathcal{H}) $. We give some propertis relating some construction of integral $K$-operator frame and operators preserving integral $K$-operator frame and we establish some new results.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85033570","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
Two families of hypercyclic nonconvolution operators 两族超循环非卷积算子
arXiv: Functional Analysis Pub Date : 2020-11-28 DOI: 10.2140/INVOLVE.2021.14.349
A. Myers, Muhammadyusuf Odinaev, David Walmsley
{"title":"Two families of hypercyclic nonconvolution operators","authors":"A. Myers, Muhammadyusuf Odinaev, David Walmsley","doi":"10.2140/INVOLVE.2021.14.349","DOIUrl":"https://doi.org/10.2140/INVOLVE.2021.14.349","url":null,"abstract":"Let $H(mathbb{C})$ be the set of all entire functions endowed with the topology of uniform convergence on compact sets. Let $lambda,binmathbb{C}$, let $C_gamma:H(mathbb{C})to H(mathbb{C})$ be the composition operator $C_gamma f(z)=f(lambda z+b)$, and let $D$ be the derivative operator. We extend results on the hypercyclicity of the non-convolution operators $T_{lambda,b}=C_gamma circ D$ by showing that whenever $|lambda|geq 1$, the algebra of operators begin{align*} {psi(T_{lambda,b}): psi(z)in H(mathbb{C}), psi(0)=0 text{ and } psi(T_{lambda,b}) text{ is continuous}} end{align*} and the family of operators begin{align*} {C_gammacircvarphi(D): varphi(z) text{ is an entire function of exponential type with } varphi(0)=0} end{align*} consist entirely of hypercyclic operators (i.e., each operator has a dense orbit).","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91391639","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
New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry 再现核希尔伯特空间的新特征及其在度量几何中的应用
arXiv: Functional Analysis Pub Date : 2020-11-18 DOI: 10.7494/OPMATH.2021.41.3.283
D. Alpay, P. Jorgensen
{"title":"New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry","authors":"D. Alpay, P. Jorgensen","doi":"10.7494/OPMATH.2021.41.3.283","DOIUrl":"https://doi.org/10.7494/OPMATH.2021.41.3.283","url":null,"abstract":"We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present ageneral positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysisand metric geometry and provide a number of examples.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89893038","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: 9
Average sampling in certain subspaces of Hilbert–Schmidt operators on $$L^2(mathbb {R}^d)$$ 上的Hilbert-Schmidt算子的子空间中的平均抽样 $$L^2(mathbb {R}^d)$$
arXiv: Functional Analysis Pub Date : 2020-11-11 DOI: 10.1007/S43670-021-00011-5
Antonio G. Garc'ia
{"title":"Average sampling in certain subspaces of Hilbert–Schmidt operators on $$L^2(mathbb {R}^d)$$","authors":"Antonio G. Garc'ia","doi":"10.1007/S43670-021-00011-5","DOIUrl":"https://doi.org/10.1007/S43670-021-00011-5","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79078563","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: 1
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