Related papers: Composition operators with surjective symbol and s…
We prove sharp uniform $L^p$-bounds for low-lying eigenfunctions of non-self-adjoint semiclassical pseudodifferential operators $P$ on $\mathbb{R}^{n}$ whose principal symbols are doubly-characteristic at the origin of $\mathbb{R}^{2n}$.…
We show that every non-compact weighted composition operator $f \mapsto u\cdot (f\circ\phi)$ acting on a Hardy space $H^p$ for $1 \leq p < \infty$ fixes an isomorphic copy of the sequence space $\ell^p$ and therefore fails to be strictly…
In this paper we propose a different (and equivalent) norm on $S^{2} ({\mathbb{D}})$ which consists of functions whose derivatives are in the Hardy space of unit disk. The reproducing kernel of $S^{2}({\mathbb{D}})$ in this norm admits an…
We identify Fock-type spaces $\mathcal{F}_{(m,p)}$ on which the differentiation operator $D$ has closed range. We prove that $D$ has closed range only if it is surjective, and this happens if and only if $m=1$. Moreover, since the operator…
We consider the bounded linear operators with domain in the Hilbert space $L^2(S^n)$, $n=2,3,5$ and describe its symbolic calculus defined by the Berezin quantization. In particular, we derive an explicit formula for the composition of…
We compare the rate of decay of singular numbers of a given composition operator acting on various Hilbert spaces of analytic functions on the unit disk $\D$. We show that for the Hardy and Bergman spaces, our results are sharp. We also…
A suffixient set is a novel combinatorial object that captures the essential information of repetitive strings in a way that, provided with a random access mechanism, supports various forms of pattern matching. In this paper, we study the…
In this paper we initiate the study of composition operators on the noncommutative Hardy space $H^2_{\bf ball}$. Several classical results about composition operators (boundedness, norm estimates, spectral properties, compactness,…
In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using…
In this paper, we consider the sum of weighted composition operator $C_{\psi_{0},\varphi_{0}}$ and the weighted composition--differentiation operator $D_{\psi_{n},\varphi_{n},n}$ on the Hardy and weighted Bergman spaces. We describe the…
In this paper, we characterize the boundedness, the compactness and the Hilbert-Schmidt property for composition operators acting from a de Branges-Rovnyak space $\mathcal H(b)$ into itself, when $b$ is a rational function in the closed…
Consider a Hermitian operator $A$ acting on a complex Hilbert space of dimension $2^n$. We show that when $A$ has small degree in the Pauli expansion, or in other words, $A$ is a local $n$-qubit Hamiltonian, its operator norm can be…
The paper deals with unbounded composition operators with infinite matrix symbols acting in $L^2$-spaces with respect to the gaussian measure on $\mathbb{R}^\infty$. We introduce weak cohyponormality classes $\EuScript{S}_{n,r}^*$ of…
A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…
The main purpose of this paper is to investigate characterizations of composition operators on Bloch and Hardy type spaces. Initially, we use general doubling weights to study the composition operators from harmonic Bloch type spaces on the…
We prove that if a small Hankel operator on the product Hardy space belongs to some Schatten class $S^p$, $p < \infty$, then it has a symbol in product BMO. In other words, the conclusion of Nehari's theorem holds under the hypothesis that…
We consider pseudodifferential operators on functions on $\R^{n+1}$ which commute with the Euler operator, and can thus be restricted to spaces of functions homogeneous of some given degree. Their symbols can be regarded as functions on a…
We establish the following results on higher order $\mathcal{S}^p$-differentiability, $1<p<\infty$, of the operator function arising from a continuous scalar function $f$ and self-adjoint operators defined on a fixed separable Hilbert…
For suitable bounded hyperconvex sets $\Omega$ in $\mathbb{C}^N$, in particular the ball or the polydisk, we give estimates for the approximation numbers of composition operators $C_\phi \colon H^2 (\Omega) \to H^2 (\Omega)$ when $\phi…
We prove a semiclassical resolvent estimate for a broad class of non-self-adjoint, non-elliptic pseudodifferential operators in the low-lying spectral regime. The proof relies on improved ellipticity properties for the symbol of the…