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REGULARITY OF AML FUNCTIONS IN TWO-DIMENSIONAL NORMED SPACES 二维赋范空间中aml函数的正则性
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-05-20 DOI: 10.1017/S1446788722000088
Sebastián Tapia-García
{"title":"REGULARITY OF AML FUNCTIONS IN TWO-DIMENSIONAL NORMED SPACES","authors":"Sebastián Tapia-García","doi":"10.1017/S1446788722000088","DOIUrl":"https://doi.org/10.1017/S1446788722000088","url":null,"abstract":"Abstract Savin [‘ \u0000$mathcal {C}^{1}$\u0000 regularity for infinity harmonic functions in two dimensions’, Arch. Ration. Mech. Anal. 3(176) (2005), 351–361] proved that every planar absolutely minimizing Lipschitz (AML) function is continuously differentiable whenever the ambient space is Euclidean. More recently, Peng et al. [‘Regularity of absolute minimizers for continuous convex Hamiltonians’, J. Differential Equations 274 (2021), 1115–1164] proved that this property remains true for planar AML functions for certain convex Hamiltonians, using some Euclidean techniques. Their result can be applied to AML functions defined in two-dimensional normed spaces with differentiable norm. In this work we develop a purely non-Euclidean technique to obtain the regularity of planar AML functions in two-dimensional normed spaces with differentiable norm.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"1 1","pages":"406 - 430"},"PeriodicalIF":0.7,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78210187","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}
引用次数: 0
LEAVITT PATH ALGEBRAS OF WEIGHTED AND SEPARATED GRAPHS 加权图和分离图的Leavitt路径代数
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-05-11 DOI: 10.1017/S1446788722000155
P. Ara
{"title":"LEAVITT PATH ALGEBRAS OF WEIGHTED AND SEPARATED GRAPHS","authors":"P. Ara","doi":"10.1017/S1446788722000155","DOIUrl":"https://doi.org/10.1017/S1446788722000155","url":null,"abstract":"Abstract In this paper, we show that Leavitt path algebras of weighted graphs and Leavitt path algebras of separated graphs are intimately related. We prove that any Leavitt path algebra \u0000$L(E,omega )$\u0000 of a row-finite vertex weighted graph \u0000$(E,omega )$\u0000 is \u0000$*$\u0000 -isomorphic to the lower Leavitt path algebra of a certain bipartite separated graph \u0000$(E(omega ),C(omega ))$\u0000 . For a general locally finite weighted graph \u0000$(E, omega )$\u0000 , we show that a certain quotient \u0000$L_1(E,omega )$\u0000 of \u0000$L(E,omega )$\u0000 is \u0000$*$\u0000 -isomorphic to an upper Leavitt path algebra of another bipartite separated graph \u0000$(E(w)_1,C(w)^1)$\u0000 . We furthermore introduce the algebra \u0000${L^{mathrm {ab}}} (E,w)$\u0000 , which is a universal tame \u0000$*$\u0000 -algebra generated by a set of partial isometries. We draw some consequences of our results for the structure of ideals of \u0000$L(E,omega )$\u0000 , and we study in detail two different maximal ideals of the Leavitt algebra \u0000$L(m,n)$\u0000 .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"191 1","pages":"1 - 25"},"PeriodicalIF":0.7,"publicationDate":"2022-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85186930","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}
引用次数: 1
RATIONAL -STABILITY OF CONTINUOUS -ALGEBRAS 连续代数的有理稳定性
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-05-10 DOI: 10.1017/s144678872200009x
Apurva Seth, P. Vaidyanathan
{"title":"RATIONAL -STABILITY OF CONTINUOUS -ALGEBRAS","authors":"Apurva Seth, P. Vaidyanathan","doi":"10.1017/s144678872200009x","DOIUrl":"https://doi.org/10.1017/s144678872200009x","url":null,"abstract":"\u0000 We show that the properties of being rationally K-stable passes from the fibres of a continuous \u0000 \u0000 \u0000 \u0000$C(X)$\u0000\u0000 \u0000 -algebra to the ambient algebra, under the assumption that the underlying space X is compact, metrizable, and of finite covering dimension. As an application, we show that a crossed product C*-algebra is (rationally) K-stable provided the underlying C*-algebra is (rationally) K-stable, and the action has finite Rokhlin dimension with commuting towers.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78369372","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}
引用次数: 0
JAZ volume 112 issue 3 Cover and Back matter jazz第112卷第3期封面和封底
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-05-10 DOI: 10.1017/s144678872100029x
{"title":"JAZ volume 112 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s144678872100029x","DOIUrl":"https://doi.org/10.1017/s144678872100029x","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"12 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83440036","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}
引用次数: 0
INDEX 指数
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-05-10 DOI: 10.1017/s1446788721000306
{"title":"INDEX","authors":"","doi":"10.1017/s1446788721000306","DOIUrl":"https://doi.org/10.1017/s1446788721000306","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"33 1","pages":"431 - 432"},"PeriodicalIF":0.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80100733","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}
引用次数: 0
JAZ volume 112 issue 3 Cover and Front matter jazz第112卷第3期封面和封面问题
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-05-10 DOI: 10.1017/s1446788721000288
{"title":"JAZ volume 112 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1446788721000288","DOIUrl":"https://doi.org/10.1017/s1446788721000288","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"61 1","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80548847","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}
引用次数: 0
MULTIPLICATION TABLES AND WORD-HYPERBOLICITY IN FREE PRODUCTS OF SEMIGROUPS, MONOIDS AND GROUPS 半群、单群和群的自由积中的乘法表和词双曲性
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-04-13 DOI: 10.1017/s1446788723000010
Carl-Fredrik Nyberg Brodda
{"title":"MULTIPLICATION TABLES AND WORD-HYPERBOLICITY IN FREE PRODUCTS OF SEMIGROUPS, MONOIDS AND GROUPS","authors":"Carl-Fredrik Nyberg Brodda","doi":"10.1017/s1446788723000010","DOIUrl":"https://doi.org/10.1017/s1446788723000010","url":null,"abstract":"\u0000 This article studies the properties of word-hyperbolic semigroups and monoids, that is, those having context-free multiplication tables with respect to a regular combing, as defined by Duncan and Gilman [‘Word hyperbolic semigroups’, Math. Proc. Cambridge Philos. Soc.136(3) (2004), 513–524]. In particular, the preservation of word-hyperbolicity under taking free products is considered. Under mild conditions on the semigroups involved, satisfied, for example, by monoids or regular semigroups, we prove that the semigroup free product of two word-hyperbolic semigroups is again word-hyperbolic. Analogously, with a mild condition on the uniqueness of representation for the identity element, satisfied, for example, by groups, we prove that the monoid free product of two word-hyperbolic monoids is word-hyperbolic. The methods are language-theoretically general, and apply equally well to semigroups, monoids or groups with a \u0000 \u0000 \u0000 \u0000$mathbf {C}$\u0000\u0000 \u0000 -multiplication table, where \u0000 \u0000 \u0000 \u0000$mathbf {C}$\u0000\u0000 \u0000 is any reversal-closed super-\u0000 \u0000 \u0000 \u0000$operatorname {mathrm {AFL}}$\u0000\u0000 \u0000 . In particular, we deduce that the free product of two groups with \u0000 \u0000 \u0000 \u0000$mathbf {ET0L}$\u0000\u0000 \u0000 with respect to indexed multiplication tables again has an \u0000 \u0000 \u0000 \u0000$mathbf {ET0L}$\u0000\u0000 \u0000 with respect to an indexed multiplication table.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"69 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89099491","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}
引用次数: 1
SOLENOIDAL MAPS, AUTOMATIC SEQUENCES, VAN DER PUT SERIES, AND MEALY AUTOMATA 螺线管图，自动序列，范德普系列，和粉自动机
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-04-06 DOI: 10.1017/S1446788722000027
R. Grigorchuk, D. Savchuk
{"title":"SOLENOIDAL MAPS, AUTOMATIC SEQUENCES, VAN DER PUT SERIES, AND MEALY AUTOMATA","authors":"R. Grigorchuk, D. Savchuk","doi":"10.1017/S1446788722000027","DOIUrl":"https://doi.org/10.1017/S1446788722000027","url":null,"abstract":"Abstract The ring $mathbb Z_{d}$ of d-adic integers has a natural interpretation as the boundary of a rooted d-ary tree $T_{d}$ . Endomorphisms of this tree (that is, solenoidal maps) are in one-to-one correspondence with 1-Lipschitz mappings from $mathbb Z_{d}$ to itself. In the case when $d=p$ is prime, Anashin [‘Automata finiteness criterion in terms of van der Put series of automata functions’,p-Adic Numbers Ultrametric Anal. Appl. 4(2) (2012), 151–160] showed that $fin mathrm {Lip}^{1}(mathbb Z_{p})$ is defined by a finite Mealy automaton if and only if the reduced coefficients of its van der Put series constitute a p-automatic sequence over a finite subset of $mathbb Z_{p}cap mathbb Q$ . We generalize this result to arbitrary integers $dgeq 2$ and describe the explicit connection between the Moore automaton producing such a sequence and the Mealy automaton inducing the corresponding endomorphism of a rooted tree. We also produce two algorithms converting one automaton to the other and vice versa. As a demonstration, we apply our algorithms to the Thue–Morse sequence and to one of the generators of the lamplighter group acting on the binary rooted tree.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"55 1","pages":"78 - 109"},"PeriodicalIF":0.7,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74849763","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}
引用次数: 0
COMPACT AND HILBERT–SCHMIDT WEIGHTED COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES 加权bergman空间上的紧和hilbert-schmidt加权复合算子
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-03-22 DOI: 10.1017/S1446788722000039
Ching-on Lo, A. Loh
{"title":"COMPACT AND HILBERT–SCHMIDT WEIGHTED COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES","authors":"Ching-on Lo, A. Loh","doi":"10.1017/S1446788722000039","DOIUrl":"https://doi.org/10.1017/S1446788722000039","url":null,"abstract":"Abstract Let u and \u0000$varphi $\u0000 be two analytic functions on the unit disk D such that \u0000$varphi (D) subset D$\u0000 . A weighted composition operator \u0000$uC_{varphi }$\u0000 induced by u and \u0000$varphi $\u0000 is defined on \u0000$A^2_{alpha }$\u0000 , the weighted Bergman space of D, by \u0000$uC_{varphi }f := u cdot f circ varphi $\u0000 for every \u0000$f in A^2_{alpha }$\u0000 . We obtain sufficient conditions for the compactness of \u0000$uC_{varphi }$\u0000 in terms of function-theoretic properties of u and \u0000$varphi $\u0000 . We also characterize when \u0000$uC_{varphi }$\u0000 on \u0000$A^2_{alpha }$\u0000 is Hilbert–Schmidt. In particular, the characterization is independent of \u0000$alpha $\u0000 when \u0000$varphi $\u0000 is an automorphism of D. Furthermore, we investigate the Hilbert–Schmidt difference of two weighted composition operators on \u0000$A^2_{alpha }$\u0000 .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"404 1","pages":"208 - 225"},"PeriodicalIF":0.7,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76482642","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}
引用次数: 0
RETRACTED - THE KRONECKER–WEYL EQUIDISTRIBUTION THEOREM AND GEODESICS IN 3-MANIFOLDS 缩回- 3流形中的kronecker-weyl等分布定理和测地线
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2022-03-21 DOI: 10.1017/s1446788721000422
J. BECK, W. W. L. CHEN
{"title":"RETRACTED - THE KRONECKER–WEYL EQUIDISTRIBUTION THEOREM AND GEODESICS IN 3-MANIFOLDS","authors":"J. BECK, W. W. L. CHEN","doi":"10.1017/s1446788721000422","DOIUrl":"https://doi.org/10.1017/s1446788721000422","url":null,"abstract":"<p>Given any rectangular polyhedron <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220617152558528-0118:S1446788721000422:S1446788721000422_inline1.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000$3$\u0000</span></span></span></span>-manifold <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220617152558528-0118:S1446788721000422:S1446788721000422_inline2.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000$mathcal {P}$\u0000</span></span></span></span> tiled with unit cubes, we find infinitely many explicit directions related to cubic algebraic numbers such that all half-infinite geodesics in these directions are uniformly distributed in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220617152558528-0118:S1446788721000422:S1446788721000422_inline3.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000$mathcal {P}$\u0000</span></span></span></span>.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531116","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}
引用次数: 0
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