Matthias Neufang
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).
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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.
Convolution Operators on Weighted Hahn Spaces
研究加权Hahn序列空间上卷积算子的有界性、紧性及乘子代数，完整刻画了谱与精细谱，并给出示例。
Arens regularity of weighted convolution algebras that arise from totally ordered semilattices
本文将Dales与Strauss关于全序半格卷积代数Arens正则性的无权结果推广到加权情形，并进一步研究其Banach代数前对偶的存在性。
Let $G$ be a discrete group, let $p\ge1$, and let $ω$ be a weight on $G$. Using the approach from [9], we provide sufficient conditions on a weight $ω$ for $\ell^p(G,ω)$ to be a Banach algebra admitting a norm-controlled inversion in the reduced C$^*$-algebra of $G$, namely $C^*_r(G)$. We show that our results can be applied to various cases including locally finite groups as well as finitely generated groups of polynomial or intermediate growth and a natural class of weights on them. These weights are of the form of polynomial or certain subexponential functions. We also consider the non-disc…
We establish sharp convolution and multiplication estimates in weighted Lebesgue, Fourier Lebesgue and modulation spaces. Especially we recover some known results.
Constructing non-AMNM weighted convolution algebras for every semilattice of infinite breadth
本文证明在任意具有无限宽度的半格上可构造权重，使生成的加权卷积代数不具备 AMNM 性质，并通过建立具有 Ramsey 理论风味的并闭集系统二分法改进了前作结果。
Trigonometric weighted generalized convolution operator associated with Fourier cosine-sine and Kontorovich-Lebedev transformations
本研究引入带三角权重γ=sin y、关联傅里叶余弦-正弦与Kontorovich-Lebedev变换的广义卷积算子，证明其在双参数Lebesgue空间的有界性，给出加权L_p范数估计并得到相关卷积积分微分方程的L_1可解条件。
Left $θ$-derivations on weighted convolution algebras
本文研究了加权卷积代数 $L_0^\infty({\Bbb R}^+, ω)^*$ 上的左 $θ$-导子，证明了其与 $θ$-导子的关系及同构条件下的非零导子不存在性，并探讨了自动连续性及相关猜想与定理。
For an increasing sequence $(ω_n)$ of algebra weights on $\mathbb R^+$ we study various properties of the Fréchet algebra $A(ω)=\bigcap_n L^1(ω_n)$ obtained as the intersection of the weighted Banach algebras $L^1(ω_n)$. We show that every endomorphism of $A(ω)$ is standard, if for all n\in\mathbb N$ there exists $m\in\mathbb N$ such that $ω_m(t)/ω_n(t)\to\infty$ as $t\to\infty$. Moreover, we characterise the continuous derivations on this algebra: If for all $n\in\mathbb N$ there exists $m\in\mathbb N$ such that $t*ω_n(t)/ω_m(t)$ is bounded on $\mathbb R^+$, then the continuous derivations on…
Let G be a locally compact group. Consider the Banach algebra L_1(G)^**, equipped with the first Arens multiplication, as well as the algebra LUC(G)^*, the dual of the space of bounded left uniformly continuous functions on G, whose product extends the convolution in the measure algebra M(G). We present (for the most interesting case of a non-compact group) completely different - in particular, direct - proofs and even obtain sharpened versions of the results, first proved by Lau-Losert and Lau, that the topological centres of the latter algebras precisely are L_1(G) and M(G), respectively. Th…
Let $ω$ be a continuous weight on $\mathbb R^+$ and let $L^1(ω)$ be the corresponding convolution algebra. By results of Grønbæk and Bade & Dales the continuous derivations from $L^1(ω)$ to its dual space $L^{\infty}(1/ω)$ are exactly the maps of the form $$(D_ϕf)(t)=\int_0^{\infty}f(s)\,\frac{s}{t+s}\,ϕ(t+s)\,ds\qquad\text{($t\in\mathbb R^+$ and $f\in L^1(ω)$)}$$ for some $ϕ\in L^{\infty}(1/ω)$. Also, every $D_ϕ$ has a unique extension to a continuous derivation $\bar{D}_ϕ:M(ω)\to L^{\infty}(1/ω)$ from the corresponding measure algebra. We show that a certain condition on $ϕ$ implies that $\b…
In this paper we show that the realization in $L^p(X,ν_\infty)$ of the nonsymmetric Ornstein-Uhlenbeck operator $L$ is sectorial for any $p\in(1,+\infty)$ and we provide an explicit sector of analyticity. Here $(X,μ_\infty,H_\infty)$ is an abstract Wiener space, i.e., $X$ is a separable Banach space, $μ_\infty$ is a centred non degenerate Gaussian measure on $X$ and $H_\infty$ is the associated Cameron-Martin space. Further, $ν_\infty$ is a weighted Gaussian measure, that is, $ν_\infty=e^{-U}μ_\infty$ where $U$ is a convex function which satisfies some minimal conditions. Our results strongly …
We discuss continuity of the twisted convolution on (weighted) Fourier modulation spaces. We use these results to establish continuity results for the twisted convolution on Lebesgue spaces. For example we prove that if $ω$ is an appropriate weight and $1\le p\le 2$, then $L^p_{(ω)}$ is an algebra under the twisted convolution.
Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application
本文通过 Young 型定理和 Saitoh 型不等式研究了高斯加权的 Fourier-cosine 卷积的有界性，获得了加权空间的新范数估计，并探讨了其在 Fredholm 第二类积分方程中的应用及可解性条件。
Let $G$ be a finitely generated group with polynomial growth, and let $\om$ be a weight, i.e. a sub-multiplicative function on $G$ with positive values. We study when the weighted group algebra $\ell^1(G,\om)$ is isomorphic to an operator algebra. We show that $\ell^1(G,\om)$ is isomorphic to an operator algebra if $\om$ is a polynomial weight with large enough degree or an exponential weight of order $0<α<1$. We will demonstrate the order of growth of $G$ plays an important role in this question. Moreover, the algebraic centre of $\ell^1(G,\om)$ is isomorphic to a $Q$-algebra and hence satisf…
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