相关论文: A characterization of differential operators in th…

Quantization and spectral properties of Toeplitz operators acting on spaces of pluriharmonic functions over bounded symmetric domains and $\mathbb C^n$ are discussed. Results are presented on the asymptotics \begin{align*} \|…

We prove a T(1) Theorem to completely characterize compactness of Calderon-Zygmund operators. The result provides sufficient and necessary conditions for the compactness of singular integral operators acting on L^p(R).

We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…

We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…

Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…

Let $\cP_n$ be the complex vector space of all polynomials of degree at most $n$. We give several characterizations of the linear operators $T\in\cL(\cP_n)$ for which there exists a constant $C > 0$ such that for all nonconstant $p\in\cP_n$…

We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space $R^m$. In both cases we obtain several properties of these polynomials, such as a…

We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz…

We study Birkhoff-James orthogonality of bounded linear operators on complex Banach spaces and obtain a complete characterization of the same. By means of introducing new definitions, we illustrate that it is possible in the complex case,…

We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…

We consider various classes of bounded operators on the Fock space $F^2$ of Gaussian square integrable entire functions over the complex plane. These include Toeplitz (type) operators, weighted composition operators, singular integral…

If $g$ is an analytic function in the unit disc $\D $ we consider the generalized Hilbert operator $\hg$ defined by {equation*}\label{H-g} \mathcal{H}_g(f)(z)=\int_0^1f(t)g'(tz)\,dt. {equation*} We study these operators acting on classical…

In this paper, we study the uniqueness of the differential-difference polynomials of entire functions on $\mathbb{C}^{n}$. We prove the following result: Let $f(z)$ be a transcendental entire function on $\mathbb{C}^{n}$ of hyper-order less…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For compact operators $T$, we give a complete…

The space of entire functions which are integrable with respect to the Gaussian weight, known also as the Fock space, is one of the preferred functional Hilbert spaces for modelling and experimenting harmonic analysis, quantum mechanics or…

Let us suppose that $\mathbb{Q}_p$ is the field of $p$-adic numbers and $\mathbb{G}$ is a split connected reductive group scheme over $\mathbb{Z}_p$. In this work we will introduce a sheaf of twisted arithmetic differential operators on the…

In this paper, we provide a complete characterization of bounded Toeplitz operators $T_f$ on the harmonic Bergman space of the unit disk, where the symbol $f$ has a polar decomposition truncated above, that commute with $T_{z+\bar{g}}$, for…

In this paper, we are concerned with conditions under which $[p(T)]^*=\bar{p}(T^*)$, where $p(z)$ is a one-variable complex polynomial, and $T$ is an unbounded, densely defined, and linear operator. Then, we deal with the validity of the…

The aim of this paper is to characterize continuous endomorphisms in the space of entire functions of exponential type of order $p>0$. Let $A_p$ denote the space of entire functions of $n$ complex variables $z\in{\mathbb C}^n$ of order $p$…

In the setting of the Fock space over the complex plane, Bauer and Lee have recently characterized commutants of Toeplitz operators with radial symbols, under the assumption that symbols have at most polynomial growth at infinity. Their…