Journal of the Australian Mathematical Society最新文献

{"title":"VISCOSITY SOLUTIONS TO THE INFINITY LAPLACIAN EQUATION WITH SINGULAR NONLINEAR TERMS","authors":"FANG LIU, HONG SUN","doi":"10.1017/s1446788724000041","DOIUrl":"https://doi.org/10.1017/s1446788724000041","url":null,"abstract":"<p>In this paper, we study the singular boundary value problem <span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319145321108-0826:S1446788724000041:S1446788724000041_eqnu1.png\"><span data-mathjax-type=\"texmath\"><span>$$ begin{align*} begin{cases} Delta_infty^h u=lambda f(x,u,Du) quad &amp;mathrm{in}; Omega, u&gt;0quad &amp;mathrm{in}; Omega, u=0 quad &amp;mathrm{on} ;partialOmega, end{cases} end{align*} $$</span></span></img></span></p><p>where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319145321108-0826:S1446788724000041:S1446788724000041_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$lambda&gt;0$</span></span></img></span></span> is a parameter, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319145321108-0826:S1446788724000041:S1446788724000041_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$h&gt;1$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319145321108-0826:S1446788724000041:S1446788724000041_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$Delta _infty ^h u=|Du|^{h-3} langle D^2uDu,Du rangle $</span></span></img></span></span> is the highly degenerate and <span>h</span>-homogeneous operator related to the infinity Laplacian. The nonlinear term <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319145321108-0826:S1446788724000041:S1446788724000041_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$f(x,t,p):Omega times (0,infty )times mathbb {R}^{n}rightarrow mathbb {R}$</span></span></img></span></span> is a continuous function and may exhibit singularity at <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319145321108-0826:S1446788724000041:S1446788724000041_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$trightarrow 0^{+}$</span></span></img></span></span>. We establish the comparison principle by the double variables method for the general equation <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319145321108-0826:S1446788724000041:S1446788724000041_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$Delta _infty ^h u=F(x,u,Du)$</span></span></img></span></span> under some conditions on the term <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319145321108-0826:S1446788724000041:S1446788724000041_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$F(x,t,p)$</span></s","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140172514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BASIC NONARCHIMEDEAN JØRGENSEN THEORY","authors":"MATTHEW CONDER, HARRIS LEUNG, JEROEN SCHILLEWAERT","doi":"10.1017/s1446788724000028","DOIUrl":"https://doi.org/10.1017/s1446788724000028","url":null,"abstract":"We prove a nonarchimedean analogue of Jørgensen’s inequality, and use it to deduce several algebraic convergence results. As an application, we show that every dense subgroup of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000028_inline1.png\" /> <jats:tex-math> ${mathrm {SL}_2}(K)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:italic>K</jats:italic> is a <jats:italic>p</jats:italic>-adic field, contains two elements that generate a dense subgroup of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000028_inline2.png\" /> <jats:tex-math> ${mathrm {SL}_2}(K)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, which is a special case of a result by Breuillard and Gelander [‘On dense free subgroups of Lie groups’, <jats:italic>J. Algebra</jats:italic>261(2) (2003), 448–467]. We also list several other related results, which are well known to experts, but not easy to locate in the literature; for example, we show that a nonelementary subgroup of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000028_inline3.png\" /> <jats:tex-math> ${mathrm {SL}_2}(K)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> over a nonarchimedean local field <jats:italic>K</jats:italic> is discrete if and only if each of its two-generator subgroups is discrete.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140172749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"FINITENESS OF CANONICAL QUOTIENTS OF DEHN QUANDLES OF SURFACES","authors":"NEERAJ K. DHANWANI, MAHENDER SINGH","doi":"10.1017/s144678872400003x","DOIUrl":"https://doi.org/10.1017/s144678872400003x","url":null,"abstract":"<p>The Dehn quandle of a closed orientable surface is the set of isotopy classes of nonseparating simple closed curves with a natural quandle structure arising from Dehn twists. In this paper, we consider the finiteness of some canonical quotients of these quandles. For a surface of positive genus, we give a precise description of the 2-quandle of its Dehn quandle. Further, with some exceptions for genus more than 2, we determine all values of <span>n</span> for which the <span>n</span>-quandle of its Dehn quandle is finite. The result can be thought of as the Dehn quandle analogue of a similar result of Hoste and Shanahan for link quandles [‘Links with finite <span>n</span>-quandles’, <span>Algebr. Geom. Topol.</span> <span>17</span>(5) (2017), 2807–2823]. We also compute the size of the smallest nontrivial quandle quotient of the Dehn quandle of a surface. Along the way, we prove that the involutory quotient of an Artin quandle is precisely the corresponding Coxeter quandle, and also determine the smallest nontrivial quotient of a braid quandle.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140097987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"RADU GROUPS ACTING ON TREES ARE CCR","authors":"LANCELOT SEMAL","doi":"10.1017/s1446788723000381","DOIUrl":"https://doi.org/10.1017/s1446788723000381","url":null,"abstract":"<p>We classify the irreducible unitary representations of closed simple groups of automorphisms of trees acting <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$2$</span></span></img></span></span>-transitively on the boundary and whose local action at every vertex contains the alternating group. As an application, we confirm Claudio Nebbia’s CCR conjecture on trees for <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$(d_0,d_1)$</span></span></img></span></span>-semi-regular trees such that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$d_0,d_1in Theta $</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$Theta $</span></span></img></span></span> is an asymptotically dense set of positive integers.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"THE -GENERATION OF THE FINITE SIMPLE ODD-DIMENSIONAL ORTHOGONAL GROUPS","authors":"MARCO ANTONIO PELLEGRINI, MARIA CHIARA TAMBURINI BELLANI","doi":"10.1017/s1446788724000016","DOIUrl":"https://doi.org/10.1017/s1446788724000016","url":null,"abstract":"The complete classification of the finite simple groups that are <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline2.png\" /> <jats:tex-math> $(2,3)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-generated is a problem which is still open only for orthogonal groups. Here, we construct <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline3.png\" /> <jats:tex-math> $(2, 3)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-generators for the finite odd-dimensional orthogonal groups <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline4.png\" /> <jats:tex-math> $Omega _{2k+1}(q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline5.png\" /> <jats:tex-math> $kgeq 4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. As a byproduct, we also obtain <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline6.png\" /> <jats:tex-math> $(2,3)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-generators for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline7.png\" /> <jats:tex-math> $Omega _{4k}^+(q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline8.png\" /> <jats:tex-math> $kgeq 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:italic>q</jats:italic> odd, and for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline9.png\" /> <jats:tex-math> $Omega _{4k+2}^pm (q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline10.png\" /> <jats:tex-math> $kgeq 4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline11.png\" /> <jats:tex-math> $qequiv pm 1~ mathrm {(mod~ 4)}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ON THE ITERATIONS AND THE ARGUMENT DISTRIBUTION OF MEROMORPHIC FUNCTIONS","authors":"JIE DING, JIANHUA ZHENG","doi":"10.1017/s1446788723000393","DOIUrl":"https://doi.org/10.1017/s1446788723000393","url":null,"abstract":"This paper consists of two parts. The first is to study the existence of a point <jats:italic>a</jats:italic> at the intersection of the Julia set and the escaping set such that <jats:italic>a</jats:italic> goes to infinity under iterates along Julia directions or Borel directions. Additionally, we find such points that approximate all Borel directions to escape if the meromorphic functions have positive lower order. We confirm the existence of such slowly escaping points under a weaker growth condition. The second is to study the connection between the Fatou set and argument distribution. In view of the filling disks, we show nonexistence of multiply connected Fatou components if an entire function satisfies a weaker growth condition. We prove that the absence of singular directions implies the nonexistence of large annuli in the Fatou set.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"THE RIEFFEL CORRESPONDENCE FOR EQUIVALENT FELL BUNDLES","authors":"S. KALISZEWSKI, JOHN QUIGG, DANA P. WILLIAMS","doi":"10.1017/s144678872300037x","DOIUrl":"https://doi.org/10.1017/s144678872300037x","url":null,"abstract":"<p>We establish a generalized Rieffel correspondence for ideals in equivalent Fell bundles.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A WEIGHTED ESTIMATE OF COMMUTATORS OF BOCHNER–RIESZ OPERATORS FOR HERMITE OPERATOR","authors":"PENG CHEN, XIXI LIN","doi":"10.1017/s1446788723000368","DOIUrl":"https://doi.org/10.1017/s1446788723000368","url":null,"abstract":"<p>Let <span>H</span> be the Hermite operator <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$-Delta +|x|^2$</span></span></img></span></span> on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {R}^n$</span></span></img></span></span>. We prove a weighted <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$L^2$</span></span></img></span></span> estimate of the maximal commutator operator <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$sup _{R&gt;0}|[b, S_R^lambda (H)](f)|$</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$ [b, S_R^lambda (H)](f) = bS_R^lambda (H) f - S_R^lambda (H)(bf) $</span></span></img></span></span> is the commutator of a BMO function <span>b</span> and the Bochner–Riesz means <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$S_R^lambda (H)$</span></span></img></span></span> for the Hermite operator <span>H</span>. As an application, we obtain the almost everywhere convergence of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$[b, S_R^lambda (H)](f)$</span></span></img></span></span> for large <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$lambda $</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline10.png\"><span data-mathjax-type=\"texmath\"><span>$fin","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139468895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"THE PRO--SOLVABLE TOPOLOGY ON A FREE GROUP","authors":"Claude Marion, P. V. Silva, Gareth Tracey","doi":"10.1017/s1446788723000162","DOIUrl":"https://doi.org/10.1017/s1446788723000162","url":null,"abstract":"\u0000 We prove that, given a finitely generated subgroup H of a free group F, the following questions are decidable: is H closed (dense) in F for the pro-(met)abelian topology? Is the closure of H in F for the pro-(met)abelian topology finitely generated? We show also that if the latter question has a positive answer, then we can effectively construct a basis for the closure, and the closure has decidable membership problem in any case. Moreover, it is decidable whether H is closed for the pro-\u0000 \u0000 \u0000 \u0000$mathbf {V}$\u0000\u0000 \u0000 topology when \u0000 \u0000 \u0000 \u0000$mathbf {V}$\u0000\u0000 \u0000 is an equational pseudovariety of finite groups, such as the pseudovariety \u0000 \u0000 \u0000 \u0000$mathbf {S}_k$\u0000\u0000 \u0000 of all finite solvable groups with derived length \u0000 \u0000 \u0000 \u0000$leq k$\u0000\u0000 \u0000 . We also connect the pro-abelian topology with the topologies defined by abelian groups of bounded exponent.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"QUALITATIVE UNCERTAINTY PRINCIPLE ON CERTAIN LIE GROUPS","authors":"ARUP CHATTOPADHYAY, DEBKUMAR GIRI, R. K. SRIVASTAVA","doi":"10.1017/s1446788723000150","DOIUrl":"https://doi.org/10.1017/s1446788723000150","url":null,"abstract":"<p>In this article, we study the recent development of the qualitative uncertainty principle on certain Lie groups. In particular, we consider that if the Weyl transform on certain step-two nilpotent Lie groups is of finite rank, then the function has to be zero almost everywhere as long as the nonvanishing set for the function has finite measure. Further, we consider that if the Weyl transform of each Fourier–Wigner piece of a suitable function on the Heisenberg motion group is of finite rank, then the function has to be zero almost everywhere whenever the nonvanishing set for each Fourier–Wigner piece has finite measure.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138716298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}