Related papers: Weakly multiplicative distributions and weighted D…

We find sufficient conditions on a compactly supported function $g$, $\supp g = [a,b]$ which guarantee that the Gabor system $$\mathcal{G}(g;\alpha,\beta)=\{e^{2\pi i \beta m x}g(x-\alpha n)\}_{m,n\in\mathbb{Z}}$$ is a frame for all $\alpha…

In this paper we prove that given a weakly almost periodic measure $\mu$ supported inside some model set $\Lambda(W)$ with closed window $W$, then the strongly almost periodic component $\mu_S$ and the null weakly almost periodic component…

We investigate multivariate integration for a space of infinitely times differentiable functions $\mathcal{F}_{s, \boldsymbol{u}} := \{f \in C^\infty [0,1]^s \mid \| f \|_{\mathcal{F}_{s, \boldsymbol{u}}} < \infty \}$, where $\| f…

We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…

For the space of unimodular lattices in a Euclidean space, we give necessary and sufficient conditions for equidistribution of expanding translates of any real-analytic submanifold under a diagonal flow. This extends the earlier result of…

H-distributions associated to weakly convergent sequences in Sobolev spaces are determined. It is shown that a weakly convergent sequence $(u_n)$ in $W^{-k,p}( \R^d)$ has the property that $\theta u_n$ converges strongly in $W^{-k,p}(\R^d)$…

Compiling essential results for non-quasianalytic ultradistribution spaces and Colombeau versions of generalized ultradistribution algebras, we analyze strong $B$- and strong $R$-association of a generalized ultradistribution…

We study the weighted compactness and boundedness of Toeplitz operators on the Fock spaces. Fix $\alpha>0$. Let $T_{\varphi}$ be the Toeplitz operator on the Fock space $F^2_{\alpha}$ over $\mathbb{C}^n$ with symbol $\varphi\in L^{\infty}$.…

Consider $G=\SL_{ d }(\mathbb R)$ and $ \Gamma=\SL_{ d }(\mathbb Z)$. It was recently shown by the second-named author \cite{s} that for some diagonal subgroups $\{g_t\}\subset G$ and unipotent subgroups $U\subset G$, $g_t$-trajectories of…

A locally compact group $ G $ is discrete if and only if the Fourier algebra $ A(G) $ has a non-zero (weakly) compact multiplier. We partially extend this result to the setting of ultraspherical hypergroups. Let $H$ be an ultraspherical…

In this paper, we prove that a compact set $K\subset \mathbb{C}^n$ is the support of a weighted equilibrium measure if and only it is not pluripolar at each of its points extending a result of Saff and Totik to higher dimensions. Thus, we…

We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak${}^*$ compact set of semimartingale measures in the pairing…

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly…

We present in this paper a new way to define weighted Sobolev spaces when the weight functions are arbitrary small. This new approach can replace the old one consisting in modifying the domain by removing the set of points where at least…

Let $u$ be a weak solution of $ (-\Delta)^m u=f $ with Dirichlet boundary conditions in a smooth bounded domain $\Omega \subset \mathbb{R}^n$. Then, the main goal of this paper is to prove the following a priori estimate: $$…

We consider two balayage constructions on the complex plane $\mathbb C$ with real axis $\mathbb R$ for $0\leq b\in \mathbb R$. Let $u\not\equiv -\infty$ be a subharmonic function on $\mathbb C$ of order…

This article discusses a unified convergence analysis of the semilinear time-dependent equation $\partial_t u + (-1)^\mathrm{m}\Delta^{\mathrm{m}}u + u^3 - u = f$ with $\mathrm{m} \in \{1,2\}$ and homogeneous Dirichlet boundary conditions.…

This work concerns superharmonic perturbations of a Gaussian measure given by a special class of positive weights in the complex plane of the form $w(z) = \exp(-|z|^2 + U^{\mu}(z))$, where $U^{\mu}(z)$ is the logarithmic potential of a…

We prove that, in the space of all probabilistic continuous functions from a probabilistic metric space G to the set $\Delta$ + of all cumulative distribution functions vanishing at 0, the space of all 1-Lipschitz functions is compact if…

We characterize all the real numbers a,b,c and 1<= p,q,r<infty such that the weighted Sobolev space W_{a,b}^(q,p)(R^N\{0}) with power weights |x|^a and |x|^b is continuously embedded into L^{r}(R^N;|x|^cdx). Furthermore, we show that this…