Related papers: Approximation theorems connected with differential…
We introduce the notion of $Q$-commuting operators which is a generalization of commuting operators. We prove a generalized version of commutant lifting theorem and Ando's dilation theorem in the context of $Q$-commuting operators.
In this paper we introduce a Fock space related to derivatives of Gelfond-Leontiev type, a class of derivatives which includes many classic examples like fractional derivatives or Dunkl operators. For this space we establish a modified…
We establish analogues of Liouville's theorem in the complex function theory, with the differential operator replaced by various difference operators. This is done generally by the extraction of (formal) Taylor coefficients using a residue…
The goal of this article and its precursor is to demonstrate, by example, the existence of "transfer operators" betweeen relative trace formulas, which generalize the scalar transfer factors of endoscopy. These transfer operators have all…
These are the lecture notes of a series of lectures on Dunkl operators. We discuss the underlying algebraic structure of the degenerate double affine Hecke algebra, intertwiners and shift operators. We apply this to Macdonald theory. We…
The purpose of this paper is to generalize a very famous result on products of normal operators, due to I. Kaplansky. The context of generalization is that of bounded hyponormal and unbounded normal operators on complex separable Hilbert…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
This paper was published in the special issue of the Journal of Inequalities and Special Functions dedicated to Professor Ivan Dimovski's contributions to different fields of mathematics: transmutation theory, special functions, integral…
Addition theorems can be constructed by doing three-dimensional Taylor expansions according to $f (\mathbf{r} + \mathbf{r}') = \exp (\mathbf{r}' \cdot \mathbf{\nabla}) f (\mathbf{r})$. Since, however, one is normally interested in addition…
In this communication, we address the problem of approximating the atoms of a parametric dictionary, commonly encountered in the context of sparse representations in "continuous" dictionaries. We focus on the case of translation-invariant…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
The Langlands functoriality conjecture, as reformulated in the "beyond endoscopy" program, predicts comparisons between the (stable) trace formulas of different groups $G_1, G_2$ for every morphism ${^LG}_1\to {^LG}_2$ between their…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
The purpose of this article is to present one and two-weight inequalities for bilinear multiplier operators in Dunkl setting with multiple Muckenhoupt weights. In order to do so, new results regarding Littlewood-Paley type theorems and…
In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function $f$ defined on the interval $[a,b]$, this formula is derived by introducing a linear combination of $f'$ computed at $n+1$…
In this paper, we will give some results on the support of Dunkl translations on compactly supported functions. Then we will define Dunkl-type $BMO$ space and Riesz transforms for Dunkl transform on $L^\infty$, and prove the boundedness of…
We explore aspects of dilation theory in the finite dimensional case and show that for a commuting $n$-tuple of operators $T=(T_1,...,T_n) $ acting on some finite dimensional Hilbert space $H$ and a compact set $X\subset \mathbb{C}^n$ the…
We discuss in which cases the Dunkl convolution of distributions, possibly both with non-compact support, can be defined and study its analytic properties. We prove results on the (singular-)support of Dunkl convolutions. Based on this, we…
For indices p and q, 1 < p <= q < infini and a linear operator L satisfying some weak-type boundedness conditions on suitable function spaces, we give in the Dunkl setting sufficient conditions on nonnegative pairs of weight functions to…
The Pseudo-Differential Operator (p.d.o.) $h_{\mu,a}$ associated with the Bessel Operator involving the symbol $a(x,y)$ whose derivatives satisfy certain growth conditions depending on some increasing sequences is studied on certain Gevrey…