Journal of Fourier Analysis and Applications最新文献_第4页

Matrix Representation of Magnetic Pseudo-Differential Operators via Tight Gabor Frames 通过紧密 Gabor 框架对磁伪微分算子进行矩阵表示

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-04-04 DOI: 10.1007/s00041-024-10072-4

Horia D. Cornean, Bernard Helffer, Radu Purice

引用次数: 0

Spherical Analysis Attached to Some m-Step Nilpotent Lie Group 附属于某些 m 阶无势李群的球面分析

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-04-02 DOI: 10.1007/s00041-024-10076-0

Silvina Campos, José García, Linda Saal

引用次数: 0

Ideals in the Convolution Algebra of Periodic Distributions 周期分布卷积代数中的理想值

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-03-27 DOI: 10.1007/s00041-024-10078-y

Amol Sasane

{"title":"Ideals in the Convolution Algebra of Periodic Distributions","authors":"Amol Sasane","doi":"10.1007/s00041-024-10078-y","DOIUrl":"https://doi.org/10.1007/s00041-024-10078-y","url":null,"abstract":"The ring of periodic distributions on (mathbb {R}^{texttt {d}}) with usual addition of distributions, and with convolution is considered. Via Fourier series expansions, this ring is isomorphic to the ring (mathcal {S}'(mathbb {Z}^{texttt {d}})) of all maps (f:mathbb {Z}^{texttt {d}}rightarrow mathbb {C}) of at most polynomial growth (that is, there exist a real number (M>0) and an integer (texttt {m}ge 0) such that ( |f(varvec{n})|le M(1+|texttt{n}_1|+cdots +|texttt {n}_{texttt {d}}|)^{texttt {m}}) for all (varvec{n}=(texttt{n}_1,cdots , texttt {n}_{texttt {d}})in mathbb {Z}^{texttt {d}})), with pointwise operations. It is shown that finitely generated ideals in (mathcal {S}'(mathbb {Z}^{texttt {d}})) are principal, and ideal membership is characterised analytically. Calling an ideal in (mathcal {S}'(mathbb {Z}^texttt{d})) fixed if there is a common index (varvec{n}in mathbb {Z}^{texttt {d}}) where each member vanishes, the fixed maximal ideals are described, and it is shown that not all maximal ideals are fixed. It is shown that finitely generated (hence principal) prime ideals in (mathcal {S}'(mathbb {Z}^{texttt {d}})) are fixed maximal ideals. The Krull dimension of (mathcal {S}'(mathbb {Z}^{texttt {d}})) is proved to be infinite, while the weak Krull dimension is shown to be equal to 1.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315028","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

Product of Sets on Varieties in Finite Fields 有限域中变量上的集合积

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-03-27 DOI: 10.1007/s00041-024-10079-x

引用次数: 0

Universal Spectra in $$Gtimes {mathbb {Z}}_p$$ $$Gtimes {mathbb {Z}}_p$$ 中的通用光谱

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-03-21 DOI: 10.1007/s00041-024-10074-2

Weiqi Zhou

引用次数: 0

A Restriction Estimate with a Log-Concavity Assumption 对数凹假定下的限制估计值

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-03-14 DOI: 10.1007/s00041-024-10073-3

Kyoungtae Moon

{"title":"A Restriction Estimate with a Log-Concavity Assumption","authors":"Kyoungtae Moon","doi":"10.1007/s00041-024-10073-3","DOIUrl":"https://doi.org/10.1007/s00041-024-10073-3","url":null,"abstract":"The purpose of this paper is to prove an optimal restriction estimate for a class of flat curves in ({mathbb {R}} ^d), (dge 3). Namely, we consider the problem of determining all the pairs (p, q) for which the (L^p-L^q) estimate holds (or a suitable Lorentz norm substitute at the endpoint, where the (L^p-L^q) estimate fails) for the extension operator associated to (gamma (t) = (t, {frac{t^2}{2!}}, ldots , {frac{t^{d-1}}{(d-1)!}}, phi (t))), (0le tle 1), with respect to the affine arclength measure. In particular, we are interested in the flat case, i.e. when (phi (t)) satisfies (phi ^{(d)}(0) = 0) for all integers (dge 1). A prototypical example is given by (phi (t) = e^{-1/t}). The paper (Bak et al., J. Aust. Math. Soc. 85:1–28, 2008) addressed precisely this problem. The examples in Bak et al. (2008) are defined recursively in terms of an integral, and they represent progressively flatter curves. Although these include arbitrarily flat curves, it is not clear if they cover, for instance, the prototypical case (phi (t) = e^{-1/t}). We will show that the desired estimate does hold for that example and indeed for a class of examples satisfying some hypotheses involving a log-concavity condition.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"81 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147117","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

One-Dimensional Discrete Hardy and Rellich Inequalities on Integers 整数上的一维离散哈代不等式和雷利克不等式

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-03-08 DOI: 10.1007/s00041-024-10070-6

Shubham Gupta

引用次数: 0

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs 多个开放弧线上边界积分算子的形状全貌

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-02-27 DOI: 10.1007/s00041-024-10071-5

José Pinto, Fernando Henríquez, Carlos Jerez-Hanckes

引用次数: 0

Cosine Sign Correlation 余弦符号相关性

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-02-08 DOI: 10.1007/s00041-024-10067-1

Shilin Dou, Ansel Goh, Kevin Liu, Madeline Legate, Gavin Pettigrew

{"title":"Cosine Sign Correlation","authors":"Shilin Dou, Ansel Goh, Kevin Liu, Madeline Legate, Gavin Pettigrew","doi":"10.1007/s00041-024-10067-1","DOIUrl":"https://doi.org/10.1007/s00041-024-10067-1","url":null,"abstract":"Fix (left{ a_1, dots , a_n right} subset {mathbb {N}}), and let x be a uniformly distributed random variable on ([0,2pi ]). The probability ({mathbb {P}}(a_1,ldots ,a_n)) that (cos (a_1 x), dots , cos (a_n x)) are either all positive or all negative is non-zero since (cos (a_i x) sim 1) for x in a neighborhood of 0. We are interested in how small this probability can be. Motivated by a problem in spectral theory, Goncalves, Oliveira e Silva, and Steinerberger proved that ({mathbb {P}}(a_1,a_2) ge 1/3) with equality if and only if (left{ a_1, a_2 right} = gcd (a_1, a_2)cdot left{ 1, 3right} ). We prove ({mathbb {P}}(a_1,a_2,a_3)ge 1/9) with equality if and only if (left{ a_1, a_2, a_3 right} = gcd (a_1, a_2, a_3)cdot left{ 1, 3, 9right} ). The pattern does not continue, as (left{ 1,3,11,33right} ) achieves a smaller value than (left{ 1,3,9,27right} ). We conjecture multiples of (left{ 1,3,11,33right} ) to be optimal for (n=4), discuss implications for eigenfunctions of Schrödinger operators (-Delta + V), and give an interpretation of the problem in terms of the lonely runner problem.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"13 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764613","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

Stable Separation of Orbits for Finite Abelian Group Actions 有限阿贝尔群作用的稳定轨道分离

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-02-05 DOI: 10.1007/s00041-024-10069-z

Jameson Cahill, Andres Contreras, Andres Contreras Hip

引用次数: 0