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Journal of Fourier Analysis and Applications最新文献

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On the Exact Spectral Factorization of Rational Matrix Functions with Applications to Paraunitary Filter Banks 论有理矩阵函数的精确谱因式分解及其在准单元滤波器库中的应用
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-07-31 DOI: 10.1007/s00041-024-10100-3
Lasha Ephremidze, Gennady Mishuris, Ilya M. Spitkovsky
{"title":"On the Exact Spectral Factorization of Rational Matrix Functions with Applications to Paraunitary Filter Banks","authors":"Lasha Ephremidze, Gennady Mishuris, Ilya M. Spitkovsky","doi":"10.1007/s00041-024-10100-3","DOIUrl":"https://doi.org/10.1007/s00041-024-10100-3","url":null,"abstract":"<p>In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available. This novel approach leverages a fundamental component of the improved algorithm for the precise design of rational paraunitary filter banks, allowing for the predetermined placement of zeros and poles. The introduced algorithm not only advances the state-of-the-art in spectral factorization but also opens new avenues for the tailored design of paraunitary filters with specific spectral properties, offering significant potential for applications in signal processing and beyond.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867747","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 Fourier Transform on Rearrangement-Invariant Spaces 重排不变空间上的傅立叶变换
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-07-24 DOI: 10.1007/s00041-024-10101-2
Ron Kerman, Rama Rawat, Rajesh K. Singh
{"title":"The Fourier Transform on Rearrangement-Invariant Spaces","authors":"Ron Kerman, Rama Rawat, Rajesh K. Singh","doi":"10.1007/s00041-024-10101-2","DOIUrl":"https://doi.org/10.1007/s00041-024-10101-2","url":null,"abstract":"<p>Let <span>(rho )</span> be a rearrangement-invariant (r.i.) norm on the set <span>(M({mathbb {R}}^n))</span> of Lebesgue-measurable functions on <span>({mathbb {R}}^n)</span> such that the space <span>(L_{rho }({mathbb {R}}^n) = left{ f in M({mathbb {R}}^n): rho (f) &lt; infty right} )</span> is an interpolation space between <span>(L_{2}({mathbb {R}}^n))</span> and <span>(L_{{infty }}({mathbb {R}}^n).)</span> The principal result of this paper asserts that given such a <span>(rho ,)</span> the inequality </p><span>$$begin{aligned} rho ({hat{f}}) le C sigma (f) end{aligned}$$</span><p>holds for any r.i. norm <span>(sigma )</span> on <span>( M({mathbb {R}}^n))</span> if and only if </p><span>$$begin{aligned} {bar{rho }} left( U f^{*} right) le C {bar{sigma }} (f^{*}). end{aligned}$$</span><p>Here, <span>({bar{rho }})</span> is the unique r.i. norm on <span>(M({mathbb {R}}_+))</span>, <span>({mathbb {R}}_+ = (0, infty ))</span>, satisfying <span>({bar{rho }}(f^{*})=rho (f))</span> and <span>(U f^{*} (t) = int _{0}^{1/t} f^{*})</span>, in which <span>(f^{*})</span> is the nonincreasing rearrangement of <i>f</i> on <span>(mathbb {R_+})</span>. Further, in this case the smallest r.i. norm <span>(sigma )</span> for which <span>(rho ( {hat{f}}) le C sigma (f))</span> holds is given by </p><span>$$begin{aligned} sigma (f) = {bar{sigma }} (f^{*}) = {bar{rho }} left( U f^{*}right) , end{aligned}$$</span><p>where, necessarily, <span>({bar{rho }} left( int _{0}^{1/t} chi _{(0, a)} right) = {bar{rho }} left( min {1/t, , a} right) &lt; infty )</span>, for all <span>(a&gt;0)</span>. We further specialize and expand these results in the contexts of Orlicz and Lorentz Gamma spaces.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782318","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
Semi-classical Pseudo-differential Operators on $$hbar mathbb {Z}^n$$ and Applications $$hbar mathbb {Z}^n$ 上的半经典伪微分算子及其应用
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-07-10 DOI: 10.1007/s00041-024-10091-1
Linda N. A. Botchway, Marianna Chatzakou, Michael Ruzhansky
{"title":"Semi-classical Pseudo-differential Operators on $$hbar mathbb {Z}^n$$ and Applications","authors":"Linda N. A. Botchway, Marianna Chatzakou, Michael Ruzhansky","doi":"10.1007/s00041-024-10091-1","DOIUrl":"https://doi.org/10.1007/s00041-024-10091-1","url":null,"abstract":"<p>In this paper we consider the semiclassical version of pseudo-differential operators on the lattice space <span>(hbar {{mathbb {Z}}^{n}})</span>. The current work is an extension of the previous work (Botchway et al. in J Funct Anal 278(11):108473, 33, 2020) and agrees with it in the limit of the parameter <span>(hbar rightarrow 1)</span>. The various representations of the operators will be studied as well as the composition, transpose, adjoint and the link between ellipticity and parametrix of operators. We also give the conditions for the <span>(ell ^p)</span>, weighted <span>(ell ^2)</span> boundedness and <span>(ell ^p)</span> compactness of operators. We investigate the relation between the classical and semi-classical quantization in the spirit of Ruzhansky and Turunen (Pseudo-differential operators and symmetries. Pseudo-differential operators, vol 2. Theory and Applications, Birkhäuser, Basel, 2010; J Fourier Anal Appl 16(6):943–982, 2010) RTspsJFAA and employ its applications to Schatten–von Neumann classes on <span>(ell ^2( hbar mathbb {Z}^n))</span>. We establish Gårding and sharp Gårding inequalities, with an application to the well-posedness of parabolic equations on the lattice <span>(hbar mathbb {Z}^n)</span>. Finally we verify that in the limiting case where <span>(hbar rightarrow 0)</span> the semi-classical calculus of pseudo-differential operators recovers the classical Euclidean calculus, but with a twist.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141575810","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
Sharp Fourier Extension on Fractional Surfaces 分数曲面上的锐傅里叶扩展
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-06-27 DOI: 10.1007/s00041-024-10099-7
Boning Di, Dunyan Yan
{"title":"Sharp Fourier Extension on Fractional Surfaces","authors":"Boning Di, Dunyan Yan","doi":"10.1007/s00041-024-10099-7","DOIUrl":"https://doi.org/10.1007/s00041-024-10099-7","url":null,"abstract":"<p>We investigate a class of Fourier extension operators on fractional surfaces <span>((xi ,|xi |^alpha ))</span> with <span>(alpha ge 2)</span>. For the corresponding <span>(alpha )</span>-Strichartz inequalities, we characterize the precompactness of extremal sequences by applying the missing mass method and bilinear restriction theory. Our result is valid in any dimension. In particular for dimension two, our result implies the existence of extremals for <span>(alpha in [2,alpha _0))</span> with some <span>(alpha _0&gt;5)</span>.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505991","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 Hadamard–Bergman Convolution on the Half-Plane 半平面上的哈达玛-伯格曼卷积
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-06-18 DOI: 10.1007/s00041-024-10097-9
Alexey Karapetyants, Armen Vagharshakyan
{"title":"The Hadamard–Bergman Convolution on the Half-Plane","authors":"Alexey Karapetyants, Armen Vagharshakyan","doi":"10.1007/s00041-024-10097-9","DOIUrl":"https://doi.org/10.1007/s00041-024-10097-9","url":null,"abstract":"<p>We introduce the Hadamard–Bergman convolution on the half-plane. We show that it exists in terms of the Hadamard product and it is commutative on the Bergman space (more appropriately called the Bergman–Jerbashian space) in the half-plane. Further, we explore mapping properties of the generalized Bergman-type operators with exponential weights in weighted Bergman spaces in the half-plane. Finally, we deduce sharp inclusions for weighted Bergman spaces, from corresponding Sobolev-type inequalities.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505992","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
Complete Left Tail Asymptotic for the Density of Branching Processes in the Schröder Case 施罗德情况下分支过程密度的完整左尾渐近线
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-06-18 DOI: 10.1007/s00041-024-10096-w
Anton A. Kutsenko
{"title":"Complete Left Tail Asymptotic for the Density of Branching Processes in the Schröder Case","authors":"Anton A. Kutsenko","doi":"10.1007/s00041-024-10096-w","DOIUrl":"https://doi.org/10.1007/s00041-024-10096-w","url":null,"abstract":"<p>For the density of Galton-Watson processes in the Schröder case, we derive a complete left tail asymptotic series consisting of power terms multiplied by periodic factors.\u0000</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529342","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
Weak-Type (1,1) Inequality for Discrete Maximal Functions and Pointwise Ergodic Theorems Along Thin Arithmetic Sets 离散极值函数的弱型 (1,1) 不等式和沿薄算术集的点式遍历定理
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-06-12 DOI: 10.1007/s00041-024-10093-z
Leonidas Daskalakis
{"title":"Weak-Type (1,1) Inequality for Discrete Maximal Functions and Pointwise Ergodic Theorems Along Thin Arithmetic Sets","authors":"Leonidas Daskalakis","doi":"10.1007/s00041-024-10093-z","DOIUrl":"https://doi.org/10.1007/s00041-024-10093-z","url":null,"abstract":"<p>We establish weak-type (1, 1) bounds for the maximal function associated with ergodic averaging operators modeled on a wide class of thin deterministic sets <i>B</i>. As a corollary we obtain the corresponding pointwise convergence result on <span>(L^1)</span>. This contributes yet another counterexample for the conjecture of Rosenblatt and Wierdl from 1991 asserting the failure of pointwise convergence on <span>(L^1)</span> of ergodic averages along arithmetic sets with zero Banach density. The second main result is a multiparameter pointwise ergodic theorem in the spirit of Dunford and Zygmund along <i>B</i> on <span>(L^p)</span>, <span>(p&gt;1)</span>, which is derived by establishing uniform oscillation estimates and certain vector-valued maximal estimates.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505990","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
Small Cap Square Function Estimates 小盘股平方函数估计值
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-06-11 DOI: 10.1007/s00041-024-10095-x
Shengwen Gan
{"title":"Small Cap Square Function Estimates","authors":"Shengwen Gan","doi":"10.1007/s00041-024-10095-x","DOIUrl":"https://doi.org/10.1007/s00041-024-10095-x","url":null,"abstract":"<p>We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form </p><span>$$begin{aligned} Vert fVert _ple C_{alpha ,p}(R) Big Vert Big (sum _{gamma in Gamma _alpha (R^{-1})}|f_gamma |^2Big )^{1/2}Big Vert _p, end{aligned}$$</span><p>where <span>(Gamma _alpha (R^{-1}))</span> is the set of small caps of width <span>(R^{-alpha })</span>. We find sharp upper and lower bounds of the constant <span>(C_{alpha ,p}(R))</span>.\u0000</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Spectrality of Infinite Convolutions in $${mathbb {R}}^d$$ $${mathbb{R}}^d$$中无限卷积的谱性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-06-01 DOI: 10.1007/s00041-024-10094-y
Wenxia Li, Zhiqiang Wang
{"title":"The Spectrality of Infinite Convolutions in $${mathbb {R}}^d$$","authors":"Wenxia Li, Zhiqiang Wang","doi":"10.1007/s00041-024-10094-y","DOIUrl":"https://doi.org/10.1007/s00041-024-10094-y","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141402634","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
Heyde Theorem for Locally Compact Abelian Groups Containing No Subgroups Topologically Isomorphic to the 2-Dimensional Torus 局部紧密阿贝尔群无拓扑同构于二维环的子群的海德定理
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-05-30 DOI: 10.1007/s00041-024-10092-0
Gennadiy Feldman
{"title":"Heyde Theorem for Locally Compact Abelian Groups Containing No Subgroups Topologically Isomorphic to the 2-Dimensional Torus","authors":"Gennadiy Feldman","doi":"10.1007/s00041-024-10092-0","DOIUrl":"https://doi.org/10.1007/s00041-024-10092-0","url":null,"abstract":"<p>We prove the following group analogue of the well-known Heyde theorem on a characterization of the Gaussian distribution on the real line. Let <i>X</i> be a second countable locally compact Abelian group containing no subgroups topologically isomorphic to the 2-dimensional torus. Let <i>G</i> be the subgroup of <i>X</i> generated by all elements of <i>X</i> of order 2 and let <span>(alpha )</span> be a topological automorphism of the group <i>X</i> such that <span>(textrm{Ker}(I+alpha )={0})</span>. Let <span>(xi _1)</span> and <span>(xi _2)</span> be independent random variables with values in <i>X</i> and distributions <span>(mu _1)</span> and <span>(mu _2)</span> with nonvanishing characteristic functions. If the conditional distribution of the linear form <span>(L_2 = xi _1 + alpha xi _2)</span> given <span>(L_1 = xi _1 + xi _2)</span> is symmetric, then <span>(mu _j)</span> are convolutions of Gaussian distributions on <i>X</i> and distributions supported in <i>G</i>. We also prove that this theorem is false if <i>X</i> is the 2-dimensional torus.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193184","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
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