Journal d'Analyse Mathématique最新文献

Local sign changes of polynomials 多项式的局部符号变化

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0344-1

Stefan Steinerberger

{"title":"Local sign changes of polynomials","authors":"Stefan Steinerberger","doi":"10.1007/s11854-024-0344-1","DOIUrl":"https://doi.org/10.1007/s11854-024-0344-1","url":null,"abstract":"The trigonometric monomial cos(〈k, x〉)on (mathbb{T}^{d}), a harmonic polynomial (p:mathbb{S}^{d-1}rightarrowmathbb{R}) of degree k and a Laplacian eigenfunction −Δf = k2f have a root in each ball of radius ∼ ∥k∥−1 or ∼ k−1, respectively. We extend this to linear combinations and show that for any trigonometric polynomials on (mathbb{T}^{d}), any polynomial p ∈ ℝ[x1,…,xd] restricted to (mathbb{S}^{d-1}) and any linear combination of global Laplacian eigenfunctions on ℝd with d ∈ {2, 3} the same property holds for any ball whose radius is given by the sum of the inverse constituent frequencies. We also refine the fact that an eigenfunction −Δφ = λφ in Ω ⊂ ℝn has a root in each B(x, αnλ−1/2) ball: the positive and negative mass in each B(x, βnλ−1/2) ball cancel when integrated against ∥x − y∥2−n.","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"197 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266659","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 the injectivity of the shifted Funk–Radon transform and related harmonic analysis 论移位 Funk-Radon 变换的注入性及相关谐波分析

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0348-x

Boris Rubin

引用次数: 0

Arc-smooth functions and cuspidality of sets 弧光函数和集合的脆性

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0337-0

Armin Rainer

引用次数: 0

Double forms: Regular elliptic bilaplacian operators 双重形式正则椭圆双拉普拉斯算子

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0343-2

Raz Kupferman, Roee Leder

引用次数: 0

A minimax theorem for locally Lipschitz functionals and applications 局部 Lipschitz 函数的最小定理及其应用

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0346-z

Marcelo F. Furtado, João Pablo P. Da Silva

引用次数: 0

A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms 涉及梯度项的准线性椭圆方程的先验估计和柳维尔式结果

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0341-4

Roberta Filippucci, Yuhua Sun, Yadong Zheng

引用次数: 0

Degree lowering for ergodic averages along arithmetic progressions 沿着算术级数降低遍历平均数的度数

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0347-y

Nikos Frantzikinakis, Borys Kuca

{"title":"Degree lowering for ergodic averages along arithmetic progressions","authors":"Nikos Frantzikinakis, Borys Kuca","doi":"10.1007/s11854-024-0347-y","DOIUrl":"https://doi.org/10.1007/s11854-024-0347-y","url":null,"abstract":"We examine the limiting behavior of multiple ergodic averages associated with arithmetic progressions whose differences are elements of a fixed integer sequence. For each ℓ, we give necessary and sufficient conditions under which averages of length ℓ of the aforementioned form have the same limit as averages of ℓ-term arithmetic progressions. As a corollary, we derive a sufficient condition for the presence of arithmetic progressions with length ℓ+1 and restricted differences in dense subsets of integers. These results are a consequence of the following general theorem: in order to verify that a multiple ergodic average is controlled by the degree d Gowers–Host–Kra seminorm, it suffices to show that it is controlled by some Gowers–Host–Kra seminorm, and that the degree d control follows whenever we have degree d + 1 control. The proof relies on an elementary inverse theorem for the Gowers–Host–Kra seminorms involving dual functions, combined with novel estimates on averages of seminorms of dual functions. We use these estimates to obtain a higher order variant of the degree lowering argument previously used to cover averages that converge to the product of integrals.","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266657","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

Perturbations of exponential maps: Non-recurrent dynamics 指数图的扰动：非循环动力学

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0340-5

Magnus Aspenberg, Weiwei Cui

引用次数: 0

Point evaluation in Paley–Wiener spaces 帕利-维纳空间中的点评估

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0338-z

Ole Fredrik Brevig, Andrés Chirre, Joaquim Ortega-Cerdà, Kristian Seip

{"title":"Point evaluation in Paley–Wiener spaces","authors":"Ole Fredrik Brevig, Andrés Chirre, Joaquim Ortega-Cerdà, Kristian Seip","doi":"10.1007/s11854-024-0338-z","DOIUrl":"https://doi.org/10.1007/s11854-024-0338-z","url":null,"abstract":"We study the norm of point evaluation at the origin in the Paley–Wiener space PWp for 0 < p < ∞, i.e., we search for the smallest positive constant C, called ({mathscr{C}}_{p}), such that the inequality (vert f(0)vert ^{p}leq C Vert fVert _{p}^{p}) holds for every f in PWp. We present evidence and prove several results supporting the following monotonicity conjecture: The function (p mapsto {mathscr{C}}_{p}/p) is strictly decreasing on the half-line (0, ∞). Our main result implies that ({mathscr{C}}_{p} < p/2) for 2 < p < ∞, and we verify numerically that ({mathscr{C}}_{p} > p/2) for 1 ≤ p < 2. We also estimate the asymptotic behavior of ({mathscr{C}}_{p}) as p → ∞ and as p → 0+. Our approach is based on expressing ({mathscr{C}}_{p}) as the solution of an extremal problem. Extremal functions exist for all 0 < p < ∞; they are real entire functions with only real zeros, and the extremal functions are known to be unique for 1 ≤ p < ∞. Following work of Hörmander and Bernhardsson, we rely on certain orthogonality relations associated with the zeros of extremal functions, along with certain integral formulas representing respectively extremal functions and general functions at the origin. We also use precise numerical estimates for the largest eigenvalue of the Landau–Pollak–Slepian operator of time-frequency concentration. A number of qualitative and quantitative results on the distribution of the zeros of extremal functions are established. In the range 1 < p < ∞, the orthogonality relations associated with the zeros of the extremal function are linked to a de Branges space. We state a number of conjectures and further open problems pertaining to ({mathscr{C}}_{p}) and the extremal functions.","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266654","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 the bandwidths of periodic approximations to discrete schrödinger operators 论离散薛定谔算子周期近似的带宽

Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0336-1

Lian Haeming

引用次数: 0