相关论文: Simple closed form Hankel transforms based on the …
We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock-Sobolev spaces on ${\mathbb C}^n$ with respect to the weight $(1+|z|)^\rho e^{-\frac{\alpha}2|z|^{2\ell}}$, for $\ell\ge 1$, $\alpha>0$ and…
We describe some examples of classical and explicit h-transforms as particular cases of a general mechanism, which is related to the existence of symmetric diffusion operators having orthogonal polynomials as spectral decomposition.
This paper considers a family of finite dimensional simple Lie superalgebras of Cartan type over a field of characteristic $p>3$, the so-called special odd contact superalgebras. First, the spanning sets are determined for the Lie…
Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. Transformations that depend not only on the sequence elements or…
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
The classical Riordan groups associated to a given commutative ring are groups of infinite matrices (called Riordan arrays) associated to pairs of formal power series in one variable. The Fundamental Theorem of Riordan Arrays relates matrix…
By prepending zeros to a given sequence Hankel determinants of backward shifts of this sequence become meaningful. We obtain some results for the sequences of Catalan numbers and of some numbers and polynomials which are related to Catalan…
The analysis of branching problems for restriction of representations brings the concept of symmetry breaking transform and holographic transform. Symmetry breaking operators decrease the number of variables in geometric models, whereas…
In this article we shall study the analytic theory and the representation theoretic interpretations of Hankel transforms and fundamental Bessel kernels of an arbitrary rank over an archimedean field.
We give a generalization of the Pascal triangle called the quasi s-Pascal triangle where the sum of the elements crossing the diagonal rays produce the s-bonacci sequence. For this, consider a lattice path in the plane whose step set is {L…
The purpose of this paper is to introduce and study the notions of $f$-rack and $f$-quandle which are obtained by twisting the usual equational identities by a map. We provide some key constructions, examples and classification of low order…
We construct a simplicial complex, the rectangle complex of a relation R, and show that it is homotopy equivalent to the Dowker complex of R. This results in a short and conceptual proof of functorial versions of Dowker's Theorem used in…
This paper aims to show that there exists a triangulation of the Heisenberg group $\mathbb{H}^n$ into singular simplexes with regularity properties on both the low-dimensional and high-dimensional layers. For low dimensions, we request our…
New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences.…
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…
In order to study the Hochschild cohomology of triangular algebras $\mathcal T$, we construct a spectral sequence, whose terms are parametrized by the length of the trajectories of the quiver associated with $\mathcal T$, and which…
In this work, we give some criteria that allow us to decide when two sequences of matrix-valued orthogonal polynomials are related via a Darboux transformation and to build explicitly such transformation. In particular, they allow us to see…
Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The…
We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this…
We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…