Acta Mathematica Hungarica最新文献

Dimension of the Radon set

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-24 DOI: 10.1007/s10474-024-01500-4

S. B. Choudhury, S. Deo, D. Gauld, S. Podder

引用次数: 0

On groups covered by relatively subnormal Černikov local systems

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-19 DOI: 10.1007/s10474-024-01486-z

E. Ingrosso, M. Trombetti

{"title":"On groups covered by relatively subnormal Černikov local systems","authors":"E. Ingrosso, M. Trombetti","doi":"10.1007/s10474-024-01486-z","DOIUrl":"10.1007/s10474-024-01486-z","url":null,"abstract":"<div>Let (mathcal L_{mathfrak F}) be the class of groups having a local system ({X_i : iin I}) of finite subgroups such that (X_i) is subnormal in (X_j) whenever (X_ileq X_j). It has been shown by Rae in \u0000[19] that the class of soluble (mathcal L_{mathfrak F})-groups is closer to the class of soluble periodic FC-groups than might be expected. The aim of this paper is to prove that, under some additional finite-rank assumptions, one can extend Rae's results to local systems of Černikov subgroups, showing for example that the locally nilpotent residual is always covered by normal Černikov subgroups of the group, and that the factor group by the Hirsch–Plotkin radical has Černikov conjugacy classes of elements (see Theorem 5.9).In [2], Reinhold Baer introduced a characteristic subgroup of a group which coincides with the hypercentre in the finite case (we call this subgroup the Baer centre of the group); actually, as shown in [4], this subgroup coincides with the hypercentre even in periodic FC-groups. Extending these results, we prove that this equivalence holds in many relevant universes of locally finite groups (see Theorem 6.2) and in particular in certain classes of locally finite groups having local systems of the above-mentioned type (see Theorem 6.9).Finally, in order to better understand the behaviour of the Baer centre in our context, we introduce and study a new class of groups that is strictly contained between the classes of periodic FC-groups and periodic BFC-groups, and that could be very useful from a computational point of view (see Section 7).\u0000</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"185 - 218"},"PeriodicalIF":0.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638457","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: 0

The affine subspace concentration inequality for centered convex bodies

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-12 DOI: 10.1007/s10474-025-01508-4

K. Eller, A. Freyer

引用次数: 0

A characterization result for compactness of semicommutators of Toeplitz operators

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-11 DOI: 10.1007/s10474-025-01513-7

R. Rajan

{"title":"A characterization result for compactness of semicommutators of Toeplitz operators","authors":"R. Rajan","doi":"10.1007/s10474-025-01513-7","DOIUrl":"10.1007/s10474-025-01513-7","url":null,"abstract":"<div>In this paper, we investigate the compactness of semicommutators of Toeplitz operators on Hardy spaces and Bergman spaces, focusing on the operators of the form (T^{H}_{|f|^{2}}-T^{H}_{f}T^{H}_{overline{f}}) and (T^{H}_{|tilde{f}|^{2}}-T^{H}_{tilde{f}}T^{H}_{overline{tilde{f}}} ), where (tilde{f}(z)=f(z^{-1})). We establish that the compactness of these operators can be characterized through the convergence of the sequence ({T^{H}_{n}(|f|^{2})-T^{H}_{n}(f)T^{H}_{n}(overline{f})}) in the sense of singular value clustering. This provides a method for determining the compactness of semicommutators by examining the corresponding Toeplitz matrices derived from the Fourier coefficients of the symbol functions.\u0000Furthermore, we identify the function space (VMO cap L^{infty}(mathbb{T})) as the largest (C^{*})-subalgebra of (L^{infty}(mathbb{T})) such that, for any (f, g in VMO cap L^{infty}(mathbb{T}) ), sequence ({T^{H}_{n}(fg)-T^{H}_{n}(f)T^{H}_{n}(g)}) converges in terms of singular value clustering. It is already known that ( VMO cap L^{infty}(mathbb{T})) is the largest (C^{*})-subalgebra of (L^{infty}(mathbb{T})) such that, for any (f, g in VMO cap L^{infty}(mathbb{T}) ), the operator (T^{H}_{fg}-T^{H}_{f}T^{H}_{g}) is compact. Similar considerations are made for Bergman spaces (A^{2}(mathbb{D})), where we obtain partial results. This work links operator theory, numerical linear algebra, and function spaces, providing new insights into the compactness properties of Toeplitz operators and their semicommutators.</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"286 - 304"},"PeriodicalIF":0.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638130","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: 0

Estimates for approximately Jensen convex functions

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-11 DOI: 10.1007/s10474-025-01512-8

G. M. Molnár, Zs. Páles

引用次数: 0

The cardinality of orthogonal exponentials for a class of self-affine measures on ( mathbb{R}^{n} ) mathbb{R}^{n} 上一类自阿芬度量的正交指数的心数

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-09 DOI: 10.1007/s10474-025-01507-5

J. L. Chen, X. Y. Yan, P. F. Zhang

{"title":"The cardinality of orthogonal exponentials for a class of self-affine measures on ( mathbb{R}^{n} )","authors":"J. L. Chen, X. Y. Yan, P. F. Zhang","doi":"10.1007/s10474-025-01507-5","DOIUrl":"10.1007/s10474-025-01507-5","url":null,"abstract":"<div>We study the cardinality of orthogonal exponential functions in (L^{2}(mu_{{R,D}})), where (mu_{{R,D}} ) is the self-affine measure generated by an expanding real matrix ( R = {rm diag}[rho_{1},rho_{2},dots,rho_{n}] ) and a finite digit set ( Dsubsetmathbb{Z}^{n} ). Let ( m ) be a prime and ( mathcal{Z}(m_{D}) ) be the set of zeros of mask polynomial ( m_{D} ) of ( D ). Suppose (mathcal{Z}(m_{D})) can be decomposed into the union of finite (mathcal{Z} _{i}(m),) where (mathcal{Z} _{i}(m)) satisfies\u0000( (mathcal{Z} _{i}(m)-mathcal{Z} _{i}(m))backslashmathbb{Z}^{n}subsetmathcal{Z} _{i}(m)subset(m^{-1}mathbb{Z}backslash mathbb{Z})^{n} ) and ( mathcal{Z} _{i}(m)nsubseteq(m_{1}^{-1}mathbb{Z}backslash mathbb{Z})^{n} ) for all integer ( m_{1}in(0,m) ), then we show that ( L^{2}(mu_{{R,D}})) admits infinite orthogonal exponential functions if and only if ( rho_{i}=(frac{m p_{i}}{q_{i}})^{frac{1}{r_{i}}} ) for some ( r_{i},p_{i},q_{i}inmathbb{N} ) with ( gcd(p_{i},q_{i})=1 ), ( i=1,2,dots,n ). Furthermore, if ( L^{2}(mu_{{R,D}})) does not admit infinite orthogonal exponential functions, we estimate the number of orthogonal exponential functions in some cases.</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 1","pages":"219 - 235"},"PeriodicalIF":0.6,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638582","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: 0

Kepler sets of linear recurrence sequences

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-08 DOI: 10.1007/s10474-025-01506-6

D. Berend, R. Kumar

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Set systems with restricted symmetric sets of Hamming distances modulo a prime number

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-08 DOI: 10.1007/s10474-025-01510-w

R. X. J. Liu

引用次数: 0

Hungarian cubes

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-08 DOI: 10.1007/s10474-025-01503-9

S. Garti

引用次数: 0

On product representations of squares

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-02-07 DOI: 10.1007/s10474-025-01505-7

T. Tao

引用次数: 0