Related papers: Dunkl convolution and elliptic regularity for Dunk…
Several spectra of analytically Riesz operators will be characterized. These results will led to prove Weyl and Browder type theorems for the aforementioned class of operators.
Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of…
This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature…
Let $L_k=-\Delta_k+V$ be the Dunk- Schr\"{o}dinger operators, where $\Delta_k=\sum_{j=1}^dT_j^2$ is the Dunkl Laplace operator associated to the dunkl operators $T_j$ on $\mathbb{R}^d$ and $V$ is a nonnegative potential function. In the…
We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…
We establish a new theory of regularity for elliptic complex valued second order equations of the form $\mathcal L=$div$A(\nabla\cdot)$, when the coefficients of the matrix $A$ satisfy a natural algebraic condition, a strengthened version…
This paper is devoted to study the approximation properties and rate of approximation of the Szasz-Mirakjan-Kantrovich-Stancu type polynomials generated by the Dunkl generalization of the exponential function with respect to q -calculus. We…
We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…
In this paper, we exhibit two matrix representations of the rational roots of generalized Fibonacci polynomials (GFPs) under convolution product, in terms of determinants and permanents, respectively. The underlying root formulas for GFPs…
We introduce a family of commuting generalised symmetries of the Dunkl--Dirac operator inspired by the Maxwell construction in harmonic analysis. We use these generalised symmetries to construct bases of the polynomial null-solutions of the…
We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…
Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…
Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean…
We generalize classical Hobson's formula concerning partial derivatives of radial functions on a Euclidean space to a formula in the Dunkl analysis. As applications we give new simple proofs of known results involving Maxwell's…
The multiplicative anomaly related to the functional regularized determinants involving products of elliptic operators is introduced and some of its properties discussed. Its relevance concerning the mathematical consistency is stressed.…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
The $S$-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of $n$-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of…
Recently a new technique in the harmonic analysis on symmetric spaces was suggested based on certain remarkable representations of affine and double affine Hecke algebras in terms of Dunkl and Demazure operators instead of Lie groups and…
We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…