Related papers: Two characterizations of Sheffer-Dunkl sequences
We describe equivariant differential characters (classifying equivariant circle bundles with connections), their prequantization, and reduction.
We consider differential operators defined as Friedrichs extensions of quadratic forms with non-smooth coefficients. We prove a two term optimal asymptotic for the Riesz means of these operators and thereby also reprove an optimal Weyl law…
Given a sequence of polynomials $(p_n)_n$, an algebra of operators $\mathcal{A}$ acting in the linear space of polynomials and an operator $D_p\in \mathcal{A}$ with $D_p(p_n)=np_n$, we form a new sequence of polynomials $(q_n)_n$ by…
We consider the most general Dunkl shift operator $L$ with the following properties: (i) $L$ is of first order in the shift operator and involves reflections; (ii) $L$ preserves the space of polynomials of a given degree; (iii) $L$ is…
In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as $\mathcal{L}_{\alpha,\mu}$-transform and generalized Stieltjes transform. In addition, we…
The isotropic Dunkl oscillator model in three-dimensional Euclidean space is considered. The system is shown to be maximally superintegrable and its symmetries are obtained by the Schwinger construction using the raising/lowering operators…
In this note, we use a basic identity, derived from the generalized doubling integrals of \cite{C-F-G-K1}, in order to explain the existence of various global Rankin-Selberg integrals for certain $L$-functions. To derive these global…
In this paper, by extending the classic stochastic integrals, we investigate three kinds of more general stochastic integrals: Lebesgue-Stieltjes integrals on predictable sets of interval type (in short: PSITs), stochastic integrals on…
It is shown that the extensions of exactly-solvable quantum mechanical problems connected with the replacement of ordinary derivatives by Dunkl ones and with that of classical orthogonal polynomials by exceptional orthogonal ones can be…
A description of the properties of \L with complex characters is given. By using these, together with the more familiar \L with real characters, it is shown how certain two dimensional lattice sums, which previously could not be put into…
Vector-valued Jack polynomials associated to the symmetric group ${\mathfrak S}_N$ are polynomials with multiplicities in an irreducible module of ${\mathfrak S}_N$ and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators…
We introduce the concept of $\D$-operators associated to a sequence of polynomials $(p_n)_n$ and an algebra $\A$ of operators acting in the linear space of polynomials. In this paper, we show that this concept is a powerful tool to generate…
In this paper, we generalize the fractional order difference operator using $l$- Pochhammer symbol and define $l$- fractional difference operator. The $l$- fractional difference operator is further used to introduce a class of difference…
We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials. As applications, we give interesting examples. In…
In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…
In this note, a new proof for the positivity of Dunkl's intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by…
The Dirac-Dunkl operator on the 2-sphere associated to the $\mathbb{Z}_2^3$ reflection group is considered. Its symmetries are found and are shown to generate the Bannai-Ito algebra. Representations of the Bannai-Ito algebra are constructed…
The theory of polynomials orthogonal with respect to one inner product is classical. We discuss the extension of this theory to multiple inner products. Examples include the Lam\'e and Heine-Stieltjes polynomials.
It has been recently discovered that exceptional families of Sturm-Liouville orthogonal polynomials exist, that generalize in some sense the classical polynomials of Hermite, Laguerre and Jacobi. In this paper we show how new families of…
Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We…