Marcel de Jeu
We argue that another proof by Trimeche of the geometrical form of the Paley-Wiener theorems for the Dunkl transform is not correct.
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Some remarks on a proof of geometrical Paley-Wiener theorems for the Dunkl transform
本文指出文献中Dunkl变换的几何Paley-Wiener定理的一个证明存在错误，并给出相应评注。
Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line
本文用初等方法证明了实直线上 Dunkl 变换对光滑函数与 L^2 函数的 Paley-Wiener 型定理，并给出 L^p 函数的 Bang 型恒等式，且对 Fourier 变换特例亦属新证明。
Paley-Wiener theorems for the Dunkl transform
本文猜想并证明了Dunkl变换的Paley-Wiener定理的几何形式，建立了Dunkl算子与Cartan运动群的联系，并用Dunkl算子显式描述不变微分算子的径向部分，进而阐明广义Bessel函数、球函数与Abel变换之间的关系。
In this paper we present another proofs of the geometrical forms of Paley-Wiener theorems for the Dunkl transform given in [15], and we prove inversion formulas for the Dunl interwining operator Vk and for its dual tVk and we deduce the expression of the representing distributions of the inverse operators vk(-1) and tvk(-1).
We investigate $λ$-Hilbert transform, $λ$-Possion integral and conjugate $λ$-Poisson integral on the atomic Hardy space in the Dunkl setting and establish a new version of Paley type inequality which extends the results in \cite{F} and \cite{ZhongKai Li 3}.
Real Paley-Wiener theorems for the linear canonical Dunkl transform
本文研究了与线性规范Dunkl变换相关的Sobolev空间及算子性质，建立了实Paley-Wiener定理，刻画了变换支撑于多项式域的平方可积函数，并发展了Boas型Paley-Wiener定理。
The purpose of this paper is to introduce a new class of singular integral operators in the Dunkl setting involving both the Euclidean metric and the Dunkl metric. Then we provide the $T1$ theorem, the criterion for the boundedness on $L^2$ for these operators. Applying this singular integral operator theory, we establish the Littlewood-Paley theory and the Dunkl-Hardy spaces. As applications, the boundedness of singular integral operators, particularly, the Dunkl-Rieze transforms, on the Dunkl-Hardy spaces is given. The $L^2$ theory and the singular integral operator theory play crucial roles…
In this paper our aim is to establish the Paley-Wiener Theorems for the Weinstein Transform. Furthermore, some applications are presents, in particular some properties for the generalized translation operator associated with the Weinstein operator are proved.
This article considers the question of how much of the mass of an element in a Paley-Wiener space can be concentracted on a given set. We seek bounds in terms of relative densities of the given set. We extend a result of Donoho and Logan from 1992 in one dimension and consider similar results in higher dimensions.
Variable Hardy spaces in the Dunkl Setting
研究在邓克尔情形下利用离散Littlewood - Paley平方函数定义新变Hardy空间，借助相关理论考虑其原子分解特征，最终获得涉及特定度量的邓克尔 - Calderón - Zygmund奇异积分的变Hardy空间有界性。
In this article, we establish first a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the $L^p\to L^p$ norm of Dunkl translations in dimension 1. Finally we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.
On discrete holomorphic Paley-Wiener spaces and sampling on the square lattice
本文研究了方格上离散整函数的再生核Hilbert空间，受经典Paley-Wiener空间启发，给出了该空间的Paley-Wiener型刻画与采样结果。
In this paper we establish a version of the Paley-Wiener theorem of Fourier analysis in the frame of the Mellin transform. We provide two different proofs, one involving complex analysis arguments, namely the Riemann surface of the logarithm and Cauchy theorems, and the other one employing a Bernstein inequality here derived for Mellin derivatives.
Weighted Bilinear Multiplier Theorems in Dunkl Setting via Singular Integrals
本文在Dunkl背景下，通过证明Littlewood-Paley型定理和多线性Calderón-Zygmund算子的加权不等式新结果，建立了具有多个Muckenhoupt权的双线性乘子算子的单权与双权不等式。
We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and we give some relationship between these spaces, Dunkl-Lebesgue spaces and Dunkl-Morrey spaces. We prove that the Hardy-Litlewood maximal function associated with the Dunkl operators is bounded on these generalized Dunkl-Morrey spaces.
Stability of concentration in the Paley-Wiener space
本文证明了 Paley-Wiener 空间中固定时间-带宽积下集中性的稳定性，通过加权集合差异控制函数距离与区间对称差，并获得了最优指数。
A remark on the Weyl quantisation of Paley-Wiener functions
本文利用 Werner-Young 不等式与量子版 Wiener 分割引理，简洁证明了紧支集 Fourier 变换的缓增分布其 Weyl 量子化属于 Schatten p 类等价于符号 L^p 可积。
Besov spaces and Schatten class Hankel operators for Hardy and Paley--Wiener spaces in higher dimensions
该研究针对高维凸区域上的Paley–Wiener空间，建立Paley–Wiener型Besov空间理论，明确Hankel算子属于Schatten类Sᵖ的充要条件，并拓展了相关结果的适用范围。
Dynamical sampling, derivatives, and interpolation formulas in the Paley--Wiener space
本文提出了一种基于傅里叶乘子算子序列的插值公式准则，并证明该结果可恢复多个经典公式。
Optimal concentration in the Paley-Wiener space
研究帕利-维纳空间中函数在有限测度集\(E\)上的\(L^{2}\)质量集中问题，基于圆上解析三角多项式再生核的普适性极限，分两步证明区间能优化集中，得出区间在该空间中优化集中的结论。
Dynamical Sampling in Graph Paley--Wiener Spaces
本文利用归一化图拉普拉斯的谱理论，在格图和有限图上研究图信号的动态采样，构造动态框架并推导重构公式，并分析迭代次数与采样分布对框架条件数的影响。
We modify the classical Paley-Wiener spaces $PW_x$ of entire functions of finite exponential type at most $x>0$, which are square integrable on the real line, via the additional condition of vanishing at finitely many complex points $z_1, ..., z_n$. We compute the reproducing kernels and relate their variations with respect to $x$ to a Krein differential system, whose coefficient (which we call the $μ$-function) and solutions have determinantal expressions. Arguments specific to the case where the "trivial zeros" $z_1, ..., z_n$ are in arithmetic progression on the imaginary axis allow us to e…
An optimization problem and point-evaluation in Paley-Wiener spaces
本文研究 Paley-Wiener 空间中关于函数点赋值的最优常数 $\mathscr{C}_p$，通过求解一个优化问题，改进了 $2<p \leq 5$ 时 $\mathscr{C}_p<p/2$ 的已知界限。
Weak Type Estimates for Square Functions of Dunkl Heat Flows
本文通过积分型Dunkl热核估计和Caldrón--Zygmund分解，证明了Dunkl热流的Littlewood--Paley--Stein平方函数的弱(1,1)有界性，延续了先前关于该函数无维L^p有界性的研究。
Sharp embeddings between weighted Paley-Wiener spaces
本文研究了加权帕莱-维纳空间间的嵌入算子范数，通过径向对称化机制将其转化为一维问题，并在特定情况下确定了锐常数和极值解。
On the boundedness of Dunkl multipliers
本文利用Littlewood-Paley-Stein理论，在乘子$m$满足修正Hörmander条件时证明了两个版本的Dunkl乘子定理，并推广了径向情形及一般乘子算子在$L^p$空间的有界性结果。
On the failure of the Nehari Theorem for Paley-Wiener spaces
该研究针对Paley-Wiener空间中的Hankel算子，证明了$\u211d^{n}$中含无穷多端点的凸集、非多面体有界凸集及二维下所有非多面体集均不满足Nehari定理，拓展了该定理的适用边界认知。
In the classical phase retrieval problem in the Paley-Wiener class $PW_L$ for $L>0$, i.e. to recover $f\in PW_L$ from $|f|$, Akutowicz, Walther, and Hofstetter independently showed that all such solutions can be obtained by flipping an arbitrary set of complex zeros across the real line. This operation is called zero-flipping and we denote by $\mathfrak{F}_a f$ the resulting function. The operator $\mathfrak{F}_a$ is defined even if $a$ is not a genuine zero of $f$, that is if we make an error on the location of the zero. Our main goal is to investigate the effect of $\mathfrak{F}_a$. We show …
On geometry of the unit ball of Paley-Wiener space over two symmetric intervals
本文研究两个对称区间上 Paley-Wiener 空间 $PW_S^1$ 单位球的几何，并在 $ρ>σ/2$ 时完整刻画其极点与暴露点。
The zeros of point evaluation extremals in Paley-Wiener spaces
该研究针对Paley-Wiener空间的点赋值极值函数φₚ，确定其零点的渐近展开，推导其傅里叶变换性质，解决了B. Green2001年提出的自卷积极值问题。
In this paper, we show that the expansions of functions from $L^p$-Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1<p<\infty$, even in the cases when they might not converge in $L^p$-norm. We thereby consider the classical Paley-Wiener spaces $PW_c^p\subset L^p(\mathcal{R})$ of functions whose Fourier transform is supported in $[-c,c]$ and Paley-Wiener like spaces $B_{α,c}^p\subset L^p(0,\infty)$ of functions whose Hankel transform $\mathcal{H}^α$ is supported in $[0,c]$.As a side product, we show the continuity of the projection oper…
Oversampling and Donoho-Logan type theorems in model spaces
本文将Paley--Wiener背景下的过采样Shannon公式和Donoho--Logan大筛定理推广到更一般的模型空间，并给出了后者嵌入$L^2(\R,μ)$空间的定量估计。
Phase symmetrization and a no-aliasing concentration principle in Paley-Wiener spaces
该研究在无混叠条件下构造性分析Donoho-Stark集中问题，通过相位对齐函数推导不等式，结合傅里叶相位对齐与几何估计证明，还推广至单位圆多项式并明确模式化集中方法的范围与局限。
We obtain Hausdorff-Young inequalities for the one-dimensional Cherednik--Opdam transform and its inverse, and we establish a real Paley-Wiener theorem for its inverse that generalizes an analogous result by N. B. Andersen for the Jacobi transform.
Point evaluation in Paley--Wiener spaces
本文研究 Paley–Wiener 空间 $PW^p$ 中原点点赋值范数的最优常数 $\mathscr{C}_p$，通过极值问题、正交关系与数值估计证明其单调性猜想，并给出渐近行为及零点分布等结果。
The de Branges spaces of entire functions generalise the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of certain entire functions. For the Paley-Wiener space, this can be chosen to be an exponential function where the phase increases linearly. As our main result, we establish a natural geometric characterisation, in terms of densities, for real sampling and interpolating sequences in the case when the derivative of the phase function merely gives a doubling measure o…
In this paper, we introduce the Bessel-Struve transform, we establish an inversion theorem of the Weyl integral transform associated with this transform, in the case of half integers, we give a characterization of the range of $\mathcal{D}(\mathbb{R})$ by Bessel-Struve transform and we prove a Schwartz-Paley-Wiener theorem on $\mathcal{E}'(\mathbb{R})$.
The Hörmander--Bernhardsson function in higher dimensions
该研究在高维Paley–Wiener空间中求点赋值算子范数，证明径向极值函数满足三阶线性ODE，推广了奇数维结果，还证明了相关插值与倒数公式。
Boundary-Weighted Fourier Inequalities for Convex Domains
该研究针对无仿射直线的凸域上Paley-Wiener空间的边界加权傅里叶不等式，刻画了多面体与球域下使不等式成立的参数三元组，还关联了球域次临界不等式与Kakeya猜想及截断Hankel算子理论。
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