Related papers: Reducing subspaces of multiplication operators on …

We study operators of multiplication by $z^k$ in Dirichlet-type spaces $D_\alpha$. We establish the existence of $k$ and $\alpha$ for which some $z^k$-invariant subspaces of $D_\alpha$ do not satisfy the wandering property. As a consequence…

Let \phi\ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set {\phi=0}.

Given any shift-invariant closed subspace $\mathcal{S}$ (aka submodule) of the Hardy space over the unit polydisc $H^2(\mathbb{D}^n)$ (where $n \geq 2$), let $R_{z_j}:=M_{z_j}|_{\mathcal{S}}$, and $E_{z_j}:=P_{\mathcal{S}}\circ ev_{z_j}$,…

The composition operator $C_{\phi_a}f=f\circ\phi_a$ on the Hardy-Hilbert space $H^2(\mathbb{D})$ with affine symbol $\phi_a(z)=az+1-a$ and $0<a<1$ has the property that the Invariant Subspace Problem for complex separable Hilbert spaces…

The weighted Bergman spaces on the polydisc, $\mathbb A^{(\lambda)}(\mathbb D^n)$, $\lambda>0,$ splits into orthogonal direct sum of subspaces $\mathbb P_{\boldsymbol p}\big(\mathbb A^{(\lambda)}(\mathbb D^n)\big)$ indexed by the partitions…

Boundedness of weighted composition operators $W_{u,\varphi}$ acting on the classical Dirichlet space $\mathcal{D}$ as $W_{u,\varphi}f= u\, (f\circ \varphi)$ is studied in terms of the multiplier space associated to the symbol $\varphi$,…

Let denote by $S(\phi)$ the extremal operator defined by the compression of the unilateral shift $S$ to the model subspace $ H(\phi)=H^{2} \ominus \phi H^{2} $ as the following $S(\phi)f(z)=P(zf(z)),$ where $P$ denotes the orthogonal…

In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be…

A topological space $G$ is said to be a {\it rectifiable space} provided that there are a surjective homeomorphism $\phi :G\times G\rightarrow G\times G$ and an element $e\in G$ such that $\pi_{1}\circ \phi =\pi_{1}$ and for every $x\in G$…

We consider Laplacian eigenfunctions on a $d-$dimensional bounded domain $M$ (or a $d-$dimensional compact manifold $M$) with Dirichlet conditions. These operators give rise to a sequence of eigenfunctions $(e_\ell)_{\ell \in \mathbb{N}}$.…

In this article we examine Dirichlet type spaces in the unit polydisc, and multipliers between these spaces. These results extend the corresponding work of G. D. Taylor in the unit disc. In addition, we consider functions on the polydisc…

In this article, we investigate the existence of closed vector subspaces (i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces $\Lambda_{\varphi,w}$, equipped with the Luxemburg norm. If a family of Orlicz functions…

V. Matache (J. Operator Theory 73(1):243--264, 2015) raised an open problem about characterizing composition operators $C_{\phi}$ on the Hardy space $H^2$ and nonzero singular measures $\mu_1$, $\mu_2$ on the unit circle such that…

Assuming that $\phi(t)=o(t^2)$ as $t\to0$, we establish a lemma on simultaneous polynomial approximation in Orlicz-Beurling-Sobolev spaces $\ell_a^{\phi}$. These spaces, endowed with the Luxemburg norm $\Vert \cdot \Vert_{\ell^{\phi}}$,…

In an arbitrary unitary 4D CFT we consider a scalar operator \phi, and the operator \phi^2 defined as the lowest dimension scalar which appears in the OPE \phi\times\phi with a nonzero coefficient. Using general considerations of OPE,…

The Lipschitz space of an infinite (locally-finite) graph is defined as the set of functions on the vertices of the graph such that the differences of the values between adjacent vertices remain bounded. In this paper we prove that this set…

Let $D$ be an indefinite quaternion division algebra over $\mathbb{Q}$. We approach the problem of bounding the sup-norms of automorphic forms $\phi$ on $D^\times(\mathbb{A})$ that belong to irreducible automorphic representations and…

In this note we give a new sufficient condition for the boundedness of the composition operator on the Dirichlet-type space on the disc, via a two dimensional change of variables formula. With the same formula, we characterise the bounded…

In this paper we study the minimality of the commutant of an analytic Toeplitz operator $M_\varphi$, when $M_\varphi$ is defined on the Hardy space $H^2(\mathbb{D})$ and $\varphi\in H^\infty(\mathbb{D})$, denotes a bounded analytic function…

We consider generalized Orlicz-Morrey spaces $M_{\Phi,\varphi}(\mathbb{R}^{n})$ including their weak versions $WM_{\Phi,\varphi}(\mathbb{R}^{n})$. We find the sufficient conditions on the pairs $(\varphi_{1},\varphi_{2})$ and $(\Phi, \Psi)$…