Abstract We consider a general twisted shift-invariant system, $V^{t}(mathcal {A})$ , consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system $V^{t}(mathcal {A})$ to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and also obtain an orthonormal sequence of twisted translates from a given Riesz sequence of twisted translates.
{"title":"TWISTED SHIFT-INVARIANT SYSTEM IN \u0000$L^2(mathbb {R}^{2N})$","authors":"Santi Ranjan Das, R. Velsamy, Radha Ramakrishnan","doi":"10.1017/nmj.2023.11","DOIUrl":"https://doi.org/10.1017/nmj.2023.11","url":null,"abstract":"Abstract We consider a general twisted shift-invariant system, \u0000$V^{t}(mathcal {A})$\u0000 , consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system \u0000$V^{t}(mathcal {A})$\u0000 to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and also obtain an orthonormal sequence of twisted translates from a given Riesz sequence of twisted translates.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"251 1","pages":"734 - 767"},"PeriodicalIF":0.8,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41480721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we present a concavity property of the minimal $L^{2}$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity, characterizations for 1-dimensional case, and a characterization for the holding of the equality in optimal $L^2$ extension problem on open Riemann surfaces with weights may not be subharmonic.
{"title":"CONCAVITY PROPERTY OF MINIMAL INTEGRALS WITH LEBESGUE MEASURABLE GAIN","authors":"Q. Guan, Zheng Yuan","doi":"10.1017/nmj.2023.12","DOIUrl":"https://doi.org/10.1017/nmj.2023.12","url":null,"abstract":"\u0000 In this article, we present a concavity property of the minimal \u0000 \u0000 \u0000 \u0000$L^{2}$\u0000\u0000 \u0000 integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity, characterizations for 1-dimensional case, and a characterization for the holding of the equality in optimal \u0000 \u0000 \u0000 \u0000$L^2$\u0000\u0000 \u0000 extension problem on open Riemann surfaces with weights may not be subharmonic.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49499886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The classical Mordell–Weil theorem implies that an abelian variety A over a number field K has only finitely many K-rational torsion points. This finitude of torsion still holds even over the cyclotomic extension $K^{mathrm {cyc}}=K{mathbb Q}^{mathrm {ab}}$ by a result of Ribet. In this article, we consider the finiteness of torsion points of an abelian variety A over the infinite algebraic extension $K_B$ obtained by adjoining the coordinates of all torsion points of an abelian variety B. Assuming the Mumford–Tate conjecture, and up to a finite extension of the base field K, we give a necessary and sufficient condition for the finiteness of $A(K_B)_{mathrm tors}$ in terms of Mumford–Tate groups. We give a complete answer when both abelian varieties have dimension at most 3, or when both have complex multiplication.
{"title":"ON THE ESSENTIAL TORSION FINITENESS OF ABELIAN VARIETIES OVER TORSION FIELDS","authors":"Jeff Achter, Lian Duan, Xiyuan Wang","doi":"10.1017/nmj.2023.19","DOIUrl":"https://doi.org/10.1017/nmj.2023.19","url":null,"abstract":"\u0000 The classical Mordell–Weil theorem implies that an abelian variety A over a number field K has only finitely many K-rational torsion points. This finitude of torsion still holds even over the cyclotomic extension \u0000 \u0000 \u0000 \u0000$K^{mathrm {cyc}}=K{mathbb Q}^{mathrm {ab}}$\u0000\u0000 \u0000 by a result of Ribet. In this article, we consider the finiteness of torsion points of an abelian variety A over the infinite algebraic extension \u0000 \u0000 \u0000 \u0000$K_B$\u0000\u0000 \u0000 obtained by adjoining the coordinates of all torsion points of an abelian variety B. Assuming the Mumford–Tate conjecture, and up to a finite extension of the base field K, we give a necessary and sufficient condition for the finiteness of \u0000 \u0000 \u0000 \u0000$A(K_B)_{mathrm tors}$\u0000\u0000 \u0000 in terms of Mumford–Tate groups. We give a complete answer when both abelian varieties have dimension at most 3, or when both have complex multiplication.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47794676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Valeria Banica, K. Hirachi, Honda, Ko, Osamu Iyama, K. Kedlaya, Akhil Mathew, Emmanuel Russ, Sho Tanimoto, Jerry L Bona, Kenji Fukaya, Shigeyuki Kondo, Ruochuan Liu, Linquan Ma, S. Mori, Shigeru Mukai, Junjiro Noguchi, Toshiaki Shoji, Akio Tamagawa, Yukinobu Toda
. We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric counterpart of the above Schur algebras in [1] specialized at q = 1.
{"title":"NMJ volume 251 Cover and Front matter","authors":"Valeria Banica, K. Hirachi, Honda, Ko, Osamu Iyama, K. Kedlaya, Akhil Mathew, Emmanuel Russ, Sho Tanimoto, Jerry L Bona, Kenji Fukaya, Shigeyuki Kondo, Ruochuan Liu, Linquan Ma, S. Mori, Shigeru Mukai, Junjiro Noguchi, Toshiaki Shoji, Akio Tamagawa, Yukinobu Toda","doi":"10.1017/nmj.2023.1","DOIUrl":"https://doi.org/10.1017/nmj.2023.1","url":null,"abstract":". We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric counterpart of the above Schur algebras in [1] specialized at q = 1.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"251 1","pages":"f1 - f3"},"PeriodicalIF":0.8,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46731351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Since the celebrated work by Cartan, distributions with small growth vector $(2,3,5)$ have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic $(2,3,5)$ -distributions and nondegenerate lines on holomorphic contact manifolds of dimension 5. We generalize this correspondence to higher dimensions by studying nondegenerate lines on holomorphic contact manifolds and the corresponding class of distributions of small growth vector $(2m, 3m, 3m+2)$ for any positive integer m.
{"title":"LINES ON HOLOMORPHIC CONTACT MANIFOLDS AND A GENERALIZATION OF \u0000$(2,3,5)$\u0000 -DISTRIBUTIONS TO HIGHER DIMENSIONS","authors":"Jun-Muk Hwang, Qifeng Li","doi":"10.1017/nmj.2023.3","DOIUrl":"https://doi.org/10.1017/nmj.2023.3","url":null,"abstract":"Abstract Since the celebrated work by Cartan, distributions with small growth vector \u0000$(2,3,5)$\u0000 have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic \u0000$(2,3,5)$\u0000 -distributions and nondegenerate lines on holomorphic contact manifolds of dimension 5. We generalize this correspondence to higher dimensions by studying nondegenerate lines on holomorphic contact manifolds and the corresponding class of distributions of small growth vector \u0000$(2m, 3m, 3m+2)$\u0000 for any positive integer m.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"251 1","pages":"652 - 668"},"PeriodicalIF":0.8,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46568727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In a previous paper, we discussed Frobenius-projective structures on projective smooth curves in positive characteristic and established a relationship between pseudo-coordinates and Frobenius-indigenous structures by means of Frobenius-projective structures. In the present paper, we discuss an “affine version” of this study of Frobenius-projective structures. More specifically, we discuss Frobenius-affine structures and establish a similar relationship between Tango functions and Frobenius-affine-indigenous structures by means of Frobenius-affine structures. Moreover, we also consider a relationship between these objects and Tango curves.
{"title":"FROBENIUS-AFFINE STRUCTURES AND TANGO CURVES","authors":"Yuichiro Hoshi","doi":"10.1017/nmj.2022.36","DOIUrl":"https://doi.org/10.1017/nmj.2022.36","url":null,"abstract":"Abstract In a previous paper, we discussed Frobenius-projective structures on projective smooth curves in positive characteristic and established a relationship between pseudo-coordinates and Frobenius-indigenous structures by means of Frobenius-projective structures. In the present paper, we discuss an “affine version” of this study of Frobenius-projective structures. More specifically, we discuss Frobenius-affine structures and establish a similar relationship between Tango functions and Frobenius-affine-indigenous structures by means of Frobenius-affine structures. Moreover, we also consider a relationship between these objects and Tango curves.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"250 1","pages":"385 - 409"},"PeriodicalIF":0.8,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48639748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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