Related papers: About the nuclearity of ${\mathcal S}_{(M_{p})}$ a…

We characterize the nuclearity of the Beurling-Bj\"{o}rck spaces $\mathcal{S}^{(\omega)}_{(\eta)}(\mathbb{R}^d)$ and $\mathcal{S}^{\{\omega\}}_{\{\eta\}}(\mathbb{R}^d)$ in terms of the defining weight functions $\omega$ and $\eta$.

We use techniques from time-frequency analysis to show that the space $\mathcal S_\omega$ of rapidly decreasing $\omega$-ultradifferentiable functions is nuclear for every weight function $\omega(t)=o(t)$ as $t$ tends to infinity. Moreover,…

We study the nuclearity of the Gelfand-Shilov spaces $\mathcal{S}^{(\mathfrak{M})}_{(\mathscr{W})}$ and $\mathcal{S}^{\{\mathfrak{M}\}}_{\{\mathscr{W}\}}$, defined via a weight (multi-)sequence system $\mathfrak{M}$ and a weight function…

Nuclearity plays an important role for the Schwartz kernel theorem to hold and in transferring the surjectivity of a linear partial differential operator from scalar-valued to vector-valued functions via tensor product theory. In this paper…

We prove new kernel theorems for a general class of Beurling-Bj\"orck type spaces. In particular, our results cover the classical Beurling-Bj\"orck spaces $\mathcal{S}^{(\omega)}_{(\eta)}$ and $\mathcal{S}^{\{\omega\}}_{\{\eta\}}$ defined…

We study nuclear embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt class and is essentially of polynomial type. Here we can extend our previous results [17,19] where we studied…

Let $\msp$ be a purely non-atomic measure space, and let $1 < p < \infty$. If $\weakLp\msp$ is isomorphic, as a Banach space, to $\weakLp\mspp$ for some purely atomic measure space $\mspp$, then there is a measurable partition $\Omega =…

In this note we study sharp sufficient conditions for the nuclearity of Fourier integral operators on $L^p$-spaces, $1< p\leq 2$. Our conditions and those presented in Cardona [2] provide a systematic investigation on the subject for all…

Let $\omega$ and $\nu$ be radial weights on the unit disc of the complex plane, and denote $\sigma=\omega^{p'}\nu^{-\frac{p'}p}$ and $\omega_x =\int_0^1 s^x \omega(s)\,ds$ for all $1\le x<\infty$. Consider the one-weight inequality…

We have constructed a Lagrangian model (SIG-OM) with coupling of sigma and omega mesons in the relativistic mean-field theory. Properties of finite nuclei and nuclear matter have been explored with the new Lagrangian model. The study shows…

For a locally compact Abelian group $G$ and a continuous weight function $\omega$ on $G$ we show that the Beurling algebra $L^1(G, \omega)$ is weakly amenable if and only if there is no nontrivial continuous group homomorphism $\phi$: $G\to…

Let $A^p_\omega$ denote the Bergman space in the unit disc induced by a radial weight~$\omega$ with the doubling property $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$. The positive Borel measures such that the…

We show that a $C^*$-algebra $A$ is nuclear iff there is a constant $K$ and $\alpha<3$ such that, for any bounded homomorphism $u\colon A \to B(H)$, there is an isomorphism $\xi\colon H\to H$ satisfying $\|\xi^{-1}\|\|\xi\| \le…

The aim of this paper is to introduce and to study the space $\mathcal{O}_{M,\omega}(\mathbb{R}^N)$ of the multipliers of the space $\mathcal{S}_{\omega}(\mathbb{R}^N)$ of the $\omega$-ultradifferentiable rapidly decreasing functions of…

We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending…

Let $\omega$ and $\nu$ be radial weights on the unit disc of the complex plane such that $\omega$ admits the doubling property $\sup_{0\le r<1}\frac{\int_r^1 \omega(s)\,ds}{\int_{\frac{1+r}{2}}^1 \omega(s)\,ds}<\infty$. Consider the one…

We study nuclear embeddings for spaces of Besov and Triebel-Lizorkin type defined on quasi-bounded domains $\Omega\subset {\mathbb R}^d$. The counterpart for such function spaces defined on bounded domains has been considered for a long…

In this paper, we consider the weighted Hardy space $\mathcal{H}^p(\omega)$ induced by an $A_1$ weight $\omega.$ We characterize the positive Borel measure $\mu$ such that the identical operator maps $\mathcal{H}^p(\omega)$ into $L^q(d\mu)$…

The possibility of extending the linear sigma-omega model by introducing a sigma-omega coupling phenomenologically is explored. It is shown that, in contrast to the usual Walecka model, not only the effective nucleon mass M* but also the…

In this paper we first prove the metric approximation property for weighted mixed-norm $L_w^{(p_1,\dots ,p_n)}$ spaces. Using Gabor frame representation this implies that the same property holds in weighted modulation and Wiener amalgam…