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Proof of the refined Dubrovin conjecture for the Lagrangian Grassmanian $LG(2,4)$ 拉格朗日格拉斯曼$LG(2,4)$的精炼杜布罗文猜想证明
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-05 DOI: arxiv-2409.03590
Fangze Sheng
{"title":"Proof of the refined Dubrovin conjecture for the Lagrangian Grassmanian $LG(2,4)$","authors":"Fangze Sheng","doi":"arxiv-2409.03590","DOIUrl":"https://doi.org/arxiv-2409.03590","url":null,"abstract":"The Dubrovin conjecture predicts a relationship between the monodromy data of\u0000the Frobenius manifold associated to the quantum cohomology of a smooth\u0000projective variety and the bounded derived category of the same variety. A\u0000refinement of this conjecture was given by Cotti, Dubrovin and Guzzetti, which\u0000is equivalent to the Gamma conjecture II proposed by Galkin, Golyshev and\u0000Iritani. The Gamma conjecture II for quadrics was proved by Hu and Ke. The\u0000Lagrangian Grassmanian $LG(2,4)$ is isomorphic to the quadric in $mathbb P^4$.\u0000In this paper, we give a new proof of the refined Dubrovin conjecture for the\u0000Lagrangian Grassmanian $LG(2,4)$ by explicit computation.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hausdorff measure and decay rate of Riesz capacity 豪斯多夫度量和里兹容量衰减率
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-04 DOI: arxiv-2409.03070
Qiuling Fan, Richard S. Laugesen
{"title":"Hausdorff measure and decay rate of Riesz capacity","authors":"Qiuling Fan, Richard S. Laugesen","doi":"arxiv-2409.03070","DOIUrl":"https://doi.org/arxiv-2409.03070","url":null,"abstract":"The decay rate of Riesz capacity as the exponent increases to the dimension\u0000of the set is shown to yield Hausdorff measure. The result applies to strongly\u0000rectifiable sets, and so in particular to submanifolds of Euclidean space. For\u0000strictly self-similar fractals, a one-sided decay estimate is found. Along the\u0000way, a purely measure theoretic proof is given for subadditivity of the\u0000reciprocal of Riesz energy.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp Fourier decay estimates for measures supported on the well-approximable numbers 可近似数上支持的度量的傅立叶衰减锐估计值
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-04 DOI: arxiv-2409.02854
Robert Fraser, Thanh Nguyen
{"title":"Sharp Fourier decay estimates for measures supported on the well-approximable numbers","authors":"Robert Fraser, Thanh Nguyen","doi":"arxiv-2409.02854","DOIUrl":"https://doi.org/arxiv-2409.02854","url":null,"abstract":"We construct a measure on the well-approximable numbers whose Fourier\u0000transform decays at a nearly optimal rate. This gives a logarithmic improvement\u0000on a previous construction of Kaufman.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximations of generalized Bernstein functions 广义伯恩斯坦函数的近似值
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-04 DOI: arxiv-2409.02536
Stamatis Koumandos, Henrik Laurberg Pedersen
{"title":"Approximations of generalized Bernstein functions","authors":"Stamatis Koumandos, Henrik Laurberg Pedersen","doi":"arxiv-2409.02536","DOIUrl":"https://doi.org/arxiv-2409.02536","url":null,"abstract":"We establish sharp inequalities involving the incomplete Beta and Gamma\u0000functions. These inequalities arise in the approximation of generalized\u0000Bernstein functions by higher order Thorin-Bernstein functions. Furthermore,\u0000new properties of a related function, namely\u0000$x^{lambda}Gamma(x)/Gamma(x+lambda)$ are derived.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"267 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On criteria for periodic wavelet frame 关于周期性小波框架的标准
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-02 DOI: arxiv-2409.01165
Anastassia Gorsanova, Elena Lebedeva
{"title":"On criteria for periodic wavelet frame","authors":"Anastassia Gorsanova, Elena Lebedeva","doi":"arxiv-2409.01165","DOIUrl":"https://doi.org/arxiv-2409.01165","url":null,"abstract":"We provide constructive necessary and sufficient conditions for a family of\u0000periodic wavelets to be a Parseval wavelet frame. The criterion generalizes\u0000unitary and oblique extension principles. It may be very useful for\u0000applications to signal processing because it allows to design any wavelet frame\u0000explicitly starting with refinable functions. The practically important case of\u0000one wavelet generator and refinable functions being trigonometric polynomials\u0000is discussed in details. As an application we study approximation properties of\u0000frames and give conditions for a coincidence of approximation orders provided\u0000by periodic multiresolution analysis and by a wavelet frame in terms of our\u0000criterion.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multilinear estimates for maximal rough singular integrals 最大粗糙奇异积分的多线性估计
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-31 DOI: arxiv-2409.00357
Bae Jun Park
{"title":"Multilinear estimates for maximal rough singular integrals","authors":"Bae Jun Park","doi":"arxiv-2409.00357","DOIUrl":"https://doi.org/arxiv-2409.00357","url":null,"abstract":"In this work, we establish $L^{p_1}times cdotstimes L^{p_1}to L^p$ bounds\u0000for maximal multi-(sub)linear singular integrals associated with homogeneous\u0000kernels $frac{Omega(vec{boldsymbol{y}}')}{|vec{boldsymbol{y}}|^{mn}}$ where $Omega$ is an $L^q$ function on the unit sphere $mathbb{S}^{mn-1}$\u0000with vanishing moment condition and $q>1$. As an application, we obtain almost everywhere convergence results for the\u0000associated doubly truncated multilinear singular integrals.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A partial-sum deformation for a family of orthogonal polynomials 正交多项式族的偏和变形
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-30 DOI: arxiv-2409.00261
Erik Koelink, Pablo Román, Wadim Zudilin
{"title":"A partial-sum deformation for a family of orthogonal polynomials","authors":"Erik Koelink, Pablo Román, Wadim Zudilin","doi":"arxiv-2409.00261","DOIUrl":"https://doi.org/arxiv-2409.00261","url":null,"abstract":"There are several questions one may ask about polynomials\u0000$q_m(x)=q_m(x;t)=sum_{n=0}^mt^mp_n(x)$ attached to a family of orthogonal\u0000polynomials ${p_n(x)}_{nge0}$. In this note we draw attention to the\u0000naturalness of this partial-sum deformation and related beautiful structures.\u0000In particular, we investigate the location and distribution of zeros of\u0000$q_m(x;t)$ in the case of varying real parameter $t$.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
$L^{p}$ estimates for multilinear maximal Bochner--Riesz means and square function 多线性最大波赫纳--里兹均值和平方函数的 $L^{p}$ 估计值
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-30 DOI: arxiv-2408.17069
Kalachand Shuin
{"title":"$L^{p}$ estimates for multilinear maximal Bochner--Riesz means and square function","authors":"Kalachand Shuin","doi":"arxiv-2408.17069","DOIUrl":"https://doi.org/arxiv-2408.17069","url":null,"abstract":"In this article we have investigated $L^{p}$ boundedness of the multilinear\u0000maximal Bochner--Riesz means and the corresponding square function. We have\u0000exploited the ideas given in the paper \"Maximal estimates for bilinear\u0000Bochner--Riesz means\" (Adv. Math. 395(2022) 108100) by Jotsaroop and\u0000Shrivastava, in order to prove our results.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Turán-Type Inequalities for Gaussian Hypergeometric Functions, and Baricz's Conjecture 高斯超几何函数的 Turán 型不等式和 Baricz 猜想
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-28 DOI: arxiv-2408.15723
Song-Liang Qiu, Xiao-Yan Ma, Xue-Yan Xiang
{"title":"Turán-Type Inequalities for Gaussian Hypergeometric Functions, and Baricz's Conjecture","authors":"Song-Liang Qiu, Xiao-Yan Ma, Xue-Yan Xiang","doi":"arxiv-2408.15723","DOIUrl":"https://doi.org/arxiv-2408.15723","url":null,"abstract":"In 2007, 'A. Baricz put forward a conjecture concerning Tur'an-type\u0000inequalities for Gaussian hypergeometric functions (see Conjecture ref{ConjA}\u0000in Section ref{Sec1}). In this paper, the authors disprove this conjecture\u0000with several methods, and present Tur'an-type double inequalities for Gaussian\u0000hypergeometric functions, and sharp bounds for complete and generalized\u0000elliptic integrals of the first kind.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chebyshev approximation of $x^m (-log x)^l$ in the interval $0le x le 1$ 在 $0le x le 1$ 的区间内对 $x^m (-log x)^l$ 进行切比雪夫近似计算
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-27 DOI: arxiv-2408.15212
Richard J. Mathar
{"title":"Chebyshev approximation of $x^m (-log x)^l$ in the interval $0le x le 1$","authors":"Richard J. Mathar","doi":"arxiv-2408.15212","DOIUrl":"https://doi.org/arxiv-2408.15212","url":null,"abstract":"The series expansion of $x^m (-log x)^l$ in terms of the shifted Chebyshev\u0000Polynomials $T_n^*(x)$ requires evaluation of the integral family $int_0^1 x^m\u0000(-log x)^l dx / sqrt{x-x^2}$. We demonstrate that these can be reduced by\u0000partial integration to sums over integrals with exponent $m=0$ which have known\u0000representations as finite sums over polygamma functions.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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