Related papers: Complex symmetric composition operators induced by…
This paper is concerned with universality properties of composition operators $C_f$, where the symbol $f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of $C_f$ when $f$ is…
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…
Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…
Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through…
By investigating which level of universality composition operators $C_f$ can have, where the symbol $f$ is given by the restriction of a transcendental entire function to suitable parts of the Fatou set of $f$, this work combines the theory…
In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional…
Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent that the question of whether weighted composition operators on…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity…
Fourier integral operators with complex phase function are an important tool in the analysis of partial differential equations. The present paper focus on the principal symbol of Lagrangian distributions with complex phase. We provide an…
In this paper, we study quasinormal and hyponormal composition operators \W with linear fractional compositional symbol $\ph$ on the Hardy and weighted Bergman spaces. We characterize the quasinormal composition operators induced on $H^{2}$…
We study the existence of a common hypercyclic vector for different families of composition operators.
In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In addition, we give…
We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar…
The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz continuity of complex-valued harmonic…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
In this paper, we initially study when an anti-linear Toeplitz operator is in the commutant of a composition operator. Primarily, we investigate weighted composition operators $W_{g,\psi}$ commuting with complex symmetric weighted…
We study composition operators between weighted Bergman spaces of the polydisc induced by smooth symbols. We prove a general result of continuity which only involves the behaviour of the symbol on the polytorus. We deduce from this several…
The paper develops a symbolic calculus for Fourier integral operators associated with canonical transformations.