Journal of Fourier Analysis and Applications最新文献_第5页

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":null,"pages":null},"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

The Turán Problem and Its Dual for Positive Definite Functions Supported on a Ball in $${mathbb {R}}^d$$ 支持$${mathbb {R}}^d$$ 球上的正定函数的图兰问题及其对偶问题

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-02-05 DOI: 10.1007/s00041-024-10068-0

Jean-Pierre Gabardo

{"title":"The Turán Problem and Its Dual for Positive Definite Functions Supported on a Ball in $${mathbb {R}}^d$$","authors":"Jean-Pierre Gabardo","doi":"10.1007/s00041-024-10068-0","DOIUrl":"https://doi.org/10.1007/s00041-024-10068-0","url":null,"abstract":"The Turán problem for an open ball of radius r centered at the origin in ({mathbb {R}}^d) consists in computing the supremum of the integrals of positive definite functions compactly supported on that ball and taking the value 1 at the origin. Siegel proved, in the 1930s that this supremum is equal to (2^{-d}) mutiplied by the Lebesgue measure of the ball and is reached by a multiple of the self-convolution of the indicator function of the ball of radius r/2. Several proofs of this result are known and, in this paper, we will provide a new proof of it based on the notion of “dual Turán problem”, a related maximization problem involving positive definite distributions. We provide, in particular, an explicit construction of the Fourier transform of a maximizer for the dual Turán problem. This approach to the problem provides a direct link between certain aspects of the theory of frames in Fourier analysis and the Turán problem. In particular, as an intermediary step needed for our main result, we construct new families of Parseval frames, involving Bessel functions, on the interval [0, 1].","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764713","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

Limited Range Extrapolation with Quantitative Bounds and Applications 带定量界限的有限范围外推法及其应用

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-01-10 DOI: 10.1007/s00041-023-10061-z

Mingming Cao, Honghai Liu, Zengyan Si, Kôzô Yabuta

{"title":"Limited Range Extrapolation with Quantitative Bounds and Applications","authors":"Mingming Cao, Honghai Liu, Zengyan Si, Kôzô Yabuta","doi":"10.1007/s00041-023-10061-z","DOIUrl":"https://doi.org/10.1007/s00041-023-10061-z","url":null,"abstract":"In recent years, sharp or quantitative weighted inequalities have attracted considerable attention on account of the (A_2) conjecture solved by Hytönen. Advances have greatly improved conceptual understanding of classical objects such as Calderón–Zygmund operators. However, plenty of operators do not fit into the class of Calderón–Zygmund operators and fail to be bounded on all (L^p(w)) spaces for (p in (1, infty )) and (w in A_p). In this paper we develop Rubio de Francia extrapolation with quantitative bounds to investigate quantitative weighted inequalities for operators beyond the (multilinear) Calderón–Zygmund theory. We mainly establish a quantitative multilinear limited range extrapolation in terms of exponents (p_i in (mathfrak {p}_i^-, mathfrak {p}_i^+)) and weights (w_i^{p_i} in A_{p_i/mathfrak {p}_i^-} cap RH_{(mathfrak {p}_i^+/p_i)'}), (i=1, ldots , m), which refines a result of Cruz-Uribe and Martell. We also present an extrapolation from multilinear operators to the corresponding commutators. Additionally, our result is quantitative and allows us to extend special quantitative estimates in the Banach space setting to the quasi-Banach space setting. Our proof is based on an off-diagonal extrapolation result with quantitative bounds. Finally, we present various applications to illustrate the utility of extrapolation by concentrating on quantitative weighted estimates for some typical multilinear operators such as bilinear Bochner–Riesz means, bilinear rough singular integrals, and multilinear Fourier multipliers. In the linear case, based on the Littlewood–Paley theory, we include weighted jump and variational inequalities for rough singular integrals.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422586","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

The Schatten Classes of Calderón–Zygmund Operators 卡尔德龙-齐格蒙德算子的沙腾类

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-01-10 DOI: 10.1007/s00041-023-10059-7

Paco Villarroya

引用次数: 0

A Class of Oscillatory Singular Integrals with Rough Kernels and Fewnomials Phases 一类具有粗糙内核和少项式相位的振荡奇积分

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-01-10 DOI: 10.1007/s00041-023-10066-8

Jiao Ma, Chenyan Wang, Huoxiong Wu

{"title":"A Class of Oscillatory Singular Integrals with Rough Kernels and Fewnomials Phases","authors":"Jiao Ma, Chenyan Wang, Huoxiong Wu","doi":"10.1007/s00041-023-10066-8","DOIUrl":"https://doi.org/10.1007/s00041-023-10066-8","url":null,"abstract":"This paper is concerned with the oscillatory singular integral operator (T_Q) defined by $$begin{aligned} T_Qf(x)=mathrm{p.v.}int _{{mathbb {R}^n}}f(x-y)frac{Omega (y)}{|y|^n}e^{iQ(|y|)}dy, end{aligned}$$where (Q(t)=sum _{1le ile m}a_it^{alpha _i}) is a real-valued polynomial on (mathbb {R}), (Omega ) is a homogenous function of degree zero on (mathbb {R}^n) with mean value zero on the unit sphere (S^{n-1}). Under the assumption of that (Omega in H^1(S^{n-1})), the authors show that (T_Q) is bounded on the weighted Lebesgue spaces (L^p(omega )) for (1<p<infty ) and (omega in tilde{A}_{p}^{I}(mathbb {R}_+)) with the uniform bound only depending on m, the number of monomials in polynomial Q, not on the degree of Q as in the previous results. This result is new even in the case (omega equiv 1), which can also be regarded as an improvement and generalization of the result obtained by Guo in [New York J. Math. 23 (2017), 1733-1738].","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422276","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

A Family of Fractal Fourier Restriction Estimates with Implications on the Kakeya Problem 分形傅里叶限制估计系列及其对 Kakeya 问题的影响

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-01-10 DOI: 10.1007/s00041-023-10065-9

Bassam Shayya

引用次数: 0

Modified Ambiguity Function and Wigner Distribution Associated With Quadratic-Phase Fourier Transform 与二次相傅里叶变换相关的修正模糊函数和维格纳分布

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-01-04 DOI: 10.1007/s00041-023-10058-8

Tien Minh Lai

引用次数: 0

Separating Fourier and Schur Multipliers 分离傅立叶乘法器和舒尔乘法器

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-01-02 DOI: 10.1007/s00041-023-10063-x

Cédric Arhancet, Christoph Kriegler, Christian Le Merdy, Safoura Zadeh

{"title":"Separating Fourier and Schur Multipliers","authors":"Cédric Arhancet, Christoph Kriegler, Christian Le Merdy, Safoura Zadeh","doi":"10.1007/s00041-023-10063-x","DOIUrl":"https://doi.org/10.1007/s00041-023-10063-x","url":null,"abstract":"Let G be a locally compact unimodular group, let (1le p<infty ), let (phi in L^infty (G)) and assume that the Fourier multiplier (M_phi ) associated with (phi ) is bounded on the noncommutative (L^p)-space (L^p(VN(G))). Then (M_phi L^p(VN(G))rightarrow L^p(VN(G))) is separating (that is, ({a^*b=ab^*=0}Rightarrow {M_phi (a)^* M_phi (b)=M_phi (a)M_phi (b)^*=0}) for any (a,bin L^p(VN(G)))) if and only if there exists (cin {mathbb {C}}) and a continuous character (psi Grightarrow {mathbb {C}}) such that (phi =cpsi ) locally almost everywhere. This provides a characterization of isometric Fourier multipliers on (L^p(VN(G))), when (pnot =2). Next, let (Omega ) be a (sigma )-finite measure space, let (phi in L^infty (Omega ^2)) and assume that the Schur multiplier associated with (phi ) is bounded on the Schatten space (S^p(L^2(Omega ))). We prove that this multiplier is separating if and only if there exist a constant (cin {mathbb {C}}) and two unitaries (alpha ,beta in L^infty (Omega )) such that (phi (s,t) =c, alpha (s)beta (t)) a.e. on (Omega ^2.) This provides a characterization of isometric Schur multipliers on (S^p(L^2(Omega ))), when (pnot =2).","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094398","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

$$L^2$$ Estimates for a Nikodym Maximal Function Associated to Space Curves 与空间曲线相关的尼科迪姆最大函数的 $L^2$$ 估计数

IF 1.2 3区数学

Journal of Fourier Analysis and Applications Pub Date : 2024-01-02 DOI: 10.1007/s00041-023-10062-y

Aswin Govindan Sheri

引用次数: 0