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The square roots of some classical operators 一些经典算子的平方根
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-09-28 DOI: 10.4064/sm210928-19-9
J. Mashreghi, M. Ptak, W. Ross
{"title":"The square roots of some classical operators","authors":"J. Mashreghi, M. Ptak, W. Ross","doi":"10.4064/sm210928-19-9","DOIUrl":"https://doi.org/10.4064/sm210928-19-9","url":null,"abstract":"In this paper we give complete descriptions of the set of square roots of certain classical operators, often providing specific formulas. The classical operators included in this discussion are the square of the unilateral shift, the Volterra operator, certain compressed shifts, the unilateral shift plus its adjoint, the Hilbert matrix, and the Cesàro operator.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48656261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Idempotents of large norm and homomorphisms of Fourier algebras 大范数的幂等项与傅立叶代数的同态
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-09-25 DOI: 10.4064/sm220111-20-1
M. Anoussis, G. Eleftherakis, A. Katavolos
{"title":"Idempotents of large norm and homomorphisms of Fourier algebras","authors":"M. Anoussis, G. Eleftherakis, A. Katavolos","doi":"10.4064/sm220111-20-1","DOIUrl":"https://doi.org/10.4064/sm220111-20-1","url":null,"abstract":"We provide necessary and sufficient conditions for the existence of idempotents of arbitrarily large norms in the Fourier algebra A(G) and the Fourier-Stieltjes algebra B(G) of a locally compact group G. We prove that the existence of idempotents of arbitrarily large norm in B(G) implies the existence of homomorphisms of arbitrarily large norm from A(H) into B(G) for every locally compact group H. A partial converse is also obtained: the existence of homomorphisms of arbitrarily large norm from A(H) into B(G) for some amenable locally compact group H implies the existence of idempotents of arbitrarily large norm in B(G).","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48035097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Products of synchronous games 同步游戏产品
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-09-24 DOI: 10.4064/sm221201-19-4
Laura Manvcinska, V. Paulsen, I. Todorov, A. Winter
{"title":"Products of synchronous games","authors":"Laura Manvcinska, V. Paulsen, I. Todorov, A. Winter","doi":"10.4064/sm221201-19-4","DOIUrl":"https://doi.org/10.4064/sm221201-19-4","url":null,"abstract":"We show that the *-algebra of the product of two synchronous games is the tensor product of the corresponding *-algebras. We prove that the product game has a perfect C*-strategy if and only if each of the individual games does, and that in this case the C*-algebra of the product game is *-isomorphic to the maximal C*-tensor product of the individual C*-algebras. We provide examples of synchronous games whose synchronous values are strictly supermultiplicative.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46337574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Some remarks on the notion of Bohr chaos and invariant measures 关于玻尔混沌和不变测度概念的几点评述
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-09-09 DOI: 10.4064/sm230103-13-5
Matan Tal
{"title":"Some remarks on the notion of Bohr chaos and invariant measures","authors":"Matan Tal","doi":"10.4064/sm230103-13-5","DOIUrl":"https://doi.org/10.4064/sm230103-13-5","url":null,"abstract":"The notion of Bohr chaos was introduced in [3, 4]. We answer a question raised in [3] of whether a non uniquely ergodic minimal system of positive topological entropy can be Bohr chaotic. We also prove that all systems with the specification property are Bohr chaotic, and by this line of thought give an independent proof (and stengthening) of theorem 1 of [3] for the case of invertible systems. In addition, we present an obstruction for Bohr chaos: a system with fewer than a continuum of ergodic invariant probability measures cannot be Bohr chaotic.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49254941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Spectrum of weighted Birkhoff average 加权Birkhoff平均谱
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-09-08 DOI: 10.4064/sm210908-19-6
Bal'azs B'ar'any, M. Rams, Ruxi Shi
{"title":"Spectrum of weighted Birkhoff average","authors":"Bal'azs B'ar'any, M. Rams, Ruxi Shi","doi":"10.4064/sm210908-19-6","DOIUrl":"https://doi.org/10.4064/sm210908-19-6","url":null,"abstract":". Let { s n } n ∈ N be a decreasing nonsummable sequence of positive reals. In this paper, we investigate the weighted Birkhoff average 1 S n P n − 1 k =0 s k φ ( T k x ) on aperiodic irreducible subshift of finite type Σ A where φ : Σ A 7→ R is a continuous potential. Firstly, we show the entropy spectrum of the weighed Birkhoff averages remains the same as that of the Birkhoff averages. Then we cal-culate the packing spectrum of the weighed Birkhoff averages. It turns out that we can have two cases, either the packing dimension of every level set equals to its Hausdorff dimension or for every nonempty level set it is equal to the packing dimension of the whole space.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46131756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Calderón–Zygmund type estimates for singular quasilinear elliptic obstacle problems with measure data 具有测量数据的奇异拟线性椭圆型障碍问题的Calderón-Zygmund型估计
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-09-02 DOI: 10.4064/sm220321-26-4
Minh-Phuong Tran, Thanh-Nhan Nguyen, Phuoc-Nguyen Huynh
{"title":"Calderón–Zygmund type estimates for singular quasilinear elliptic obstacle problems with measure data","authors":"Minh-Phuong Tran, Thanh-Nhan Nguyen, Phuoc-Nguyen Huynh","doi":"10.4064/sm220321-26-4","DOIUrl":"https://doi.org/10.4064/sm220321-26-4","url":null,"abstract":"We deal with a global Calder'on-Zygmund type estimate for elliptic obstacle problems of $p$-Laplacian type with measure data. For this paper, we focus on the singular case of growth exponent, i.e. $1<p le 2-frac{1}{n}$. In addition, the emphasis of this paper is in obtaining the Lorentz bounds for the gradient of solutions with the use of fractional maximal operators.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46719388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Poisson process and sharp constants in $L^p$ and Schauder estimates for a class of degenerate Kolmogorov operators 一类退化Kolmogorov算子在$L^p$和Schauder估计中的Poisson过程和尖锐常数
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-07-13 DOI: 10.4064/sm210819-13-4
L. Marino, S. Menozzi, E. Priola
{"title":"Poisson process and sharp constants in $L^p$ and Schauder estimates for a class of degenerate Kolmogorov operators","authors":"L. Marino, S. Menozzi, E. Priola","doi":"10.4064/sm210819-13-4","DOIUrl":"https://doi.org/10.4064/sm210819-13-4","url":null,"abstract":"We consider a possibly degenerate Kolmogorov-Ornstein-Uhlenbeck operator of the form L = Tr(BD2) + 〈Az, D〉, where A, B are N × N matrices, z ∈ RN , N ≥ 1, which satisfy the Kalman condition which is equivalent to the hypoellipticity condition. We prove the following stability result: the Schauder and Sobolev estimates associated with the corresponding parabolic Cauchy problem remain valid, with the same constant, for the parabolic Cauchy problem associated with a second order perturbation of L, namely for L + Tr(S(t)D2) where S(t) is a non-negative definite N × N matrix depending continuously on t ∈ [0, T ]. Our approach relies on the perturbative technique based on the Poisson process introduced in [15].","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45119558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Mazur–Ulam property for uniform algebras 一致代数的Mazur–Ulam性质
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-07-04 DOI: 10.4064/sm210703-11-9
O. Hatori
{"title":"The Mazur–Ulam property for uniform algebras","authors":"O. Hatori","doi":"10.4064/sm210703-11-9","DOIUrl":"https://doi.org/10.4064/sm210703-11-9","url":null,"abstract":"We give a sufficient condition for a Banach space with which the homogeneous extension of a surjective isometry from the unit sphere of it onto another one is real-linear. The condition is satisfied by a uniform algebra and a certain extremely $C$-regular space of real-valued continuous functions.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43880612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Interpolation for analytic families of multilinear operators on metric measure spaces 度量测度空间上多元线性算子解析族的插值
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-07-01 DOI: 10.4064/sm210630-11-1
L. Grafakos, E. Ouhabaz
{"title":"Interpolation for analytic families of multilinear operators on metric measure spaces","authors":"L. Grafakos, E. Ouhabaz","doi":"10.4064/sm210630-11-1","DOIUrl":"https://doi.org/10.4064/sm210630-11-1","url":null,"abstract":"Let (Xj , dj , μj), j = 0, 1, . . . ,m be metric measure spaces. Given 0 < pκ ≤ ∞ for κ = 1, . . . ,m and an analytic family of multilinear operators Tz : L 1(X1)× · · ·L m (Xm)→ Lloc(X0), for z in the complex unit strip, we prove a theorem in the spirit of Stein’s complex interpolation for analytic families. Analyticity and our admissibility condition are defined in the weak (integral) sense and relax the pointwise definitions given in [9]. Continuous functions with compact support are natural dense subspaces of Lebesgue spaces over metric measure spaces and we assume the operators Tz are initially defined on them. Our main lemma concerns the approximation of continuous functions with compact support by similar functions that depend analytically in an auxiliary parameter z. An application of the main theorem concerning bilinear estimates for Schrödinger operators on Lp is included.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48909396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Sobolev spaces with non-isotropic dilations andsquare functions of Marcinkiewicz type 具有非各向同性扩张和Marcinkiewicz型平方函数的Sobolev空间
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-06-23 DOI: 10.4064/sm210819-19-3
Shuichi Sato
{"title":"Sobolev spaces with non-isotropic dilations and\u0000square functions of Marcinkiewicz type","authors":"Shuichi Sato","doi":"10.4064/sm210819-19-3","DOIUrl":"https://doi.org/10.4064/sm210819-19-3","url":null,"abstract":"We consider the weighted Sobolev spaces associated with nonisotropic dilations of Calderón-Torchinsky and characterize the spaces by the square functions of Marcinkiewicz type including those defined with repeated uses of averaging operation.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43791876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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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