We obtain an intertwining relation between some Riemann-Liouville operators of order α ∈ (1, 2), connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely asymmetric α−stable Lévy processes. An alternative approach based on recurrent extensions of positive self-similar Markov processes and exponential functionals of Lévy processes is also ...

The Segal–Shale–Weil representation associates to a symplectic transformation of the Heisenberg group an intertwining operator, called metaplectic operator. We develop an explicit construction of metaplectic operators for the Heisenberg group H(G) of a finite abelian group G, an important setting in finite time-frequency analysis. Our approach also yields a simple construction for the multivari...

In this paper we prove inversion formulas for the Dunkl intertwining operator Vk and for its dual tVk and we deduce the expression of the representing distributions of the inverse operators V −1 k and V −1 k , and we give some applications.

In this paper, we show that for a hyponormal operator the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result: Let T be a operator with property (δ) on a Banach space X and let S be a hyponormal operator on a Hilbert space H. Then every generalized intertwining linear operator θ : X → H for (S, T ) is continuous if and only ...

The operator that intertwines between the $\mathbb{Z}_2$ - Dunkl and derivative is shown to have a realization in terms of oscillator operators one dimension. This observation rests on fact intertwining maps Hermite polynomials generalized polynomials.

Motivated by the harmonic analysis of selfaffine measures, we introduce a class representations Cuntz algebra associated to random walks on graphs. The are constructed using dilation theory row coisometries. We study these representations, their commutant and intertwining operators.

The purpose of this note is to define and construct highest weight modules for Felder’s elliptic quantum groups. This is done by using exchange matrices for intertwining operators between modules over quantum affine algebras. A similar problem for the elliptic quantum group corresponding to Belavin’s R-matrix was posed in [7]. This problem, as well as its analogue for Felder’s R-matrix was solv...

We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this construction also establishes the operator product expansion for intertwining operators, which correspond to chiral vertex operators, and more generally, it establi...