Jan Pachl
Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on an arbitrary topological group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We determine multiplication and convolution topological algebras for classes of $ω$-ultradifferentiable functions of Beurling type. Hypocontinuity and discontinuity of the multiplication and convolution mappings are also investigated.
The dual space of the C*-algebra of bounded uniformly continuous functions on a uniform space carries several natural topologies. One of these is the topology of uniform convergence on bounded uniformly equicontinuous sets, or the UEB topology for short. In the particular case of a topological group and its right uniformity, the UEB topology plays a significant role in the continuity of convolution. In this paper we derive a useful characterisation of bounded uniformly equicontinuous sets on locally compact groups. Then we demonstrate that for every locally compact group G the UEB topology on …
A topological group is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the group with its right uniformity is contained in an ambit. For n=0,1,2,..., every locally aleph_n bounded topological group is either precompact or ambitable. In the familiar semigroups constructed over ambitable groups, topological centres have an effective characterization.
Let G be a locally compact non-compact group. We show that under a very mild assumption on the weight function w, the weighted group algebra L_1(G,w) is strongly Arens irregular in the sense of Dales-Lamb-Lau. To this end, we first derive a general factorization theorem for bounded families in the L_\infty(G,1/w)^*-module L_\infty(G,1/w).
Nonexistence of Frame Measures for Separated Uniform Consecutive-Digit Bernoulli Convolutions
该研究证明，当满足特定整数条件且 $N$ 不整除 $B$ 时，分离均匀连续数字伯努利卷积对应的 $N$-伯努利卷积不存在框架测度，其证明引入了适配连续数字框架多特征结构的新循环掩码商障碍。
The uniform norm on a uniform normed Q-algebra is the only uniform Q-algebra norm on it. The uniform norm on a regular uniform normed Q-algebra with unit is the only uniform norm on it. Let A be a uniform topological algebra whose spectrum M (A) is equicontinuous, then A is a uniform normed algebra. Let A be a regular semisimple commutative Banach algebra, then every algebra norm on A is a Q-algebra norm on A.
In this paper we introduce a new family of topological convolution algebras of the form $\bigcup_{p\in\mathbb N} L_2(S,μ_p)$, where $S$ is a Borel semi-group in a locally compact group $G$, which carries an inequality of the type $\|f*g\|_p\le A_{p,q}\|f\|_q\|g\|_p$ for $p > q+d$ where $d$ pre-assigned, and $A_{p,q}$ is a constant. We give a sufficient condition on the measures $μ_p$ for such an inequality to hold. We study the functional calculus and the spectrum of the elements of these algebras, and present two examples, one in the setting of non commutative stochastic distributions, and th…
Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the semigroup is contained in an ambit. In the convolution algebras constructed over ambitable semigroups, topological centres have a tractable characterization.
Let $E$ be a complete uniform topological algebra with Arens-Michael normed factors $\left(E_α\right)_{α\inΛ}.$ Then $M\left(E\right) \cong \varprojlim M\left(E_α\right)$ within an algebra isomorphism $φ$. If each factor $E_α$ is complete, then every multiplier of $E$ is continuous and $φ$ is a topological algebra isomorphism where $M\left(E\right)$ is endowed with its seminorm topology.
We prove a uniformly continuous linear extension principle in topological vector spaces from which we derive a very short and canonical construction of the Lebesgue integral of Banach space valued maps on a finite measure space. The Vitali Convergence Theorem and the Riesz-Fischer Theorem are shown to follow as easy consequences from our construction.
We prove that the additive group $(E^\ast,τ_k(E))$ of an $\mathscr{L}_\infty$-Banach space $E$, with the topology $τ_k(E)$ of uniform convergence on compact subsets of $E$, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is \emph{unitarily representable}). This is the same as proving that the topological group $(E^\ast,τ_k(E))$ is uniformly homeomorphic to a subset of $\ell_2^κ$ for some $κ$. As an immediate consequence, preduals of commutative von Neumann algebras or duals of commutative $C^\ast$-algebras are unitarily representable in the topology of uni…
We present a unified theory for the almost periodicity of functions with values in an arbitrary Banach space, measures and distributions via almost periodic elements for the action of a locally compact abelian group on a uniform topological space. We discuss the relation between Bohr and Bochner type almost periodicity, and similar conditions, and how the equivalence among such conditions relates to properties of the group action and the uniformity. We complete the paper by demonstrating how various examples considered earlier all fit in our framework.
We establish a characterization of amenability for general Hausdorff topological groups in terms of matchings with respect to finite uniform coverings. Furthermore, we prove that it suffices to just consider two-element uniform coverings. We also show that extremely amenable as well as compactly approximable topological groups satisfy a perfect matching property condition -- the latter even with regard to arbitrary uniform coverings. Finally, we prove that the automorphism group of a Fraïssé limit of a metric Fraïssé class is amenable if and only if the considered metric Fraïssé class has a ce…
On the Properties of a Bernoulli--Uniform Boolean Convolution Family
本文研究由对称伯努利分布与均匀分布的布尔卷积构成的单参数概率测度族，利用布尔能量变换推导显式公式与洛朗展开，计算累积量、矩及渐近估计，并分析其解析性质与缩放极限，证明该族不构成半群。
Let the measure algebra of a topological group be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly continuous if and only if the group has the SIN property.
We characterize topological (and uniform) spaces whose free (locally convex) topological vector spaces have a local $\mathfrak G$-base. A topological space $X$ has a local $\mathfrak G$-base if every point $x$ of $X$ has a neighborhood base $(U_α)_{α\inω^ω}$ such that $U_β\subset U_α$ for all $α\leβ$ in $ω^ω$. To construct $\mathfrak G$-bases in free topological vector spaces, we exploit a new description of the topology of a free topological vector space over a topological (or more generally, uniform) space.
We prove that the Grand Lebesgue Space, builded on a unimodular locally compact topological group, forms a Banach algebra relative to the convolution.
In a convolution semigroup over a locally compact group, measurability of the translation by a fixed element implies continuity. In other words, the measurable centre coincides with the topological centre.
Topological Amenability of Semihypergroups
本文在局部紧半超群中引入拓扑顺从性概念，通过概率测度收敛、卷积全变差及测度代数性质给出多种刻画，并证明子半超群的拓扑顺从性，解决了J. Wong于1980年提出的开放问题。
We study topologically invariant means on $L^{\infty}(\mathbb{R})$, the set of all essentially bounded functions on the real line, and prove that invariance with respect to a single convolution operator is sufficient for a mean to be topologically invariant. We also consider some applications of this result to summability methods. In particular, the notion of almost convergence is introduced for a function in $L^{\infty}(\mathbb{R})$, and a Tauberian theorem concerning almost convergence and a summability method defined by a Wiener kernel is obtained. Further, for the $C_{\infty}$ summability …
In this paper we provide necessary and sufficient conditions for the $\textnormal{weak}(1,p)$ boundedness, $1< p<\infty,$ of convolution operators on locally compact (Hausdorff) topological groups. So, we generalize a classical result due to Sobolev-Hardy-Littlewood and Stepanov. Applications to Fourier multipliers on Lie groups also are given.
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with $α$-Hölder derivatives (for some $0<α\leq 1$). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function $f$ which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of $Δ$-convex ${\Cal{C}}^{1,α}$ functions converging uniformly on bounded sets to $f$ and preserving the infimum and the set of minimizers of $f$. The techniques we d…
Let X, Y, and Z be topological modules over a topological ring R. In this paper, we introduce three different classes of bounded bigroup homomorphisms from X \times Y into Z with respect to the three different uniform convergence topologies. We show that the operations of addition and module multiplication are continuous for each class of bounded bigroup homomorphisms. Also, we investigate whether each class of bounded bigroup homomorphisms is uniformly complete.
There are many deep results on the structure of REGULAR probability measures $P(G)$ on compact/locally compact, Hausdorff topological groups G. See, for instance, the classic monographs by KR Parthasarathy, Ulf Grenander, A.Mukherjea and Nicolas A.Tserpes. It is known that the set $P(G)$ forms a semi-group under convolution. Wendel in his remarkable paper, proved a basic result regarding support of convolution of two probability measures. Consequently, he established that the semi-group $P(G)$ is not a group. In this short paper, it is proved that for a compact topological group G, the semi-gr…
Let $G$ be a locally compact group and $μ$ be a measure on $G$. In this paper we find conditions for the convolution operators $λ_p(μ)$, defined on $L^p(G)$ and given by convolution by $μ$, to be mean ergodic and uniformly mean ergodic. The ergodic properties of the operators $λ_p(μ)$ are related to the ergodic properties of the measure $μ$ as well.
Free positive multiplicative Brownian motion and the free additive convolution of semicircle and uniform distribution
本文通过计算半圆分布与均匀分布自由加性卷积的矩，为自由正乘性布朗运动谱分布的新表示提供了一个新证明，并推广了涉及 Laguerre 多项式的已知矩公式。
A discrete group $\G$ is called rigidly symmetric if the projective tensor product between the convolution algebra $\ell^1(\G)$ and any $C^*$-algebra $\A$ is symmetric. We show that in each topologically graded $C^*$-algebra over a rigidly symmetric group there is a $\ell^1$-type symmetric Banach $^*$-algebra, which is inverse closed in the $C^*$-algebra. This includes new general classes, as algebras admitting dual actions and partial crossed products. Results including convolution dominated kernels, inverse closedness with respect with ideals or weighted versions of the $\ell^1$-decay are in…
A Note on the Uniform Ergodicity of Dynamical Systems
本文研究了不可逆拓扑与保测动力系统的一致遍历性，证明其分别等价于最终周期性和周期性，并通过对格同态长期行为的分析得出结论。
Quantitative rigidity of the Wasserstein contraction under convolution
本文研究了 Wasserstein 距离在卷积下的收缩性质，通过扩展均匀凸性结果到 $p=1$，揭示了其在数学优化和概率论中的应用意义。
We establish the condition $(Ω)$ for smooth kernels of various types of convolution and differential operators. By the $(DN)$-$(Ω)$ splitting theorem of Vogt and Wagner, this implies that these operators are surjective on the corresponding spaces of vector-valued smooth functions with values in a product of Montel $(DF)$-spaces whose strong duals satisfy the condition $(DN)$, e.g., the space $\mathscr{D}'(Y)$ of distributions over an open set $Y \subseteq \mathbb{R}^n$ or the space $\mathscr{S}'(\mathbb{R}^n)$ of tempered distributions. Most notably, we show that: $(i)$ $\mathscr{E}_P(X) = \{ …
Recent results of M.Junge and Q.Xu on the ergodic properties of the averages of kernels in noncommutative L^p-spaces are applied to the analysis of the almost uniform convergence of operators induced by the convolutions on compact quantum groups.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。