Related papers: Differential processes generated by two interpolat…
We study conditions so that the determinantal point process $\Lambda_\phi$ associated to a generalized Fock space defined by a doubling subharmonic weight $\phi$ is almost surely a separated sequence in $\mathbb C$. Under a natural…
We formulate and prove a version of the celebrated Coifman-Rochberg-Weiss commutator theorem for the real method of interpolation
Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
Our starting point is a lemma due to Varopoulos. We give a different proof of a generalized form this lemma, that yields an equivalent description of the $K$-functional for the interpolation couple $(X_0,X_1)$ where…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
We study interpolating sequences of $d$-tuples of matrices, by looking at the commuting and the non-commuting case separately. In both cases, we will give a characterization of such sequences in terms of separation conditions on suitable…
In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order…
Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems abd determines the…
We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the $\mathfrak{su}(1,1)$ current algebra. We introduce raising, lowering, and neutral…
Given $E_0, E_1, F_0, F_1, E$ rearrangement invariant function spaces, $a_0$, $a_1$, $b_0$, $b_1$, $b$ slowly varying functions and $0< \theta_0<\theta_1<1$, we characterize the interpolation spaces $$(\overline{X}^{\mathcal…
Dunkl operators are differential-difference operators parametrized by a finite reflection group and a weight function. The commutative algebra generated by these operators generalizes the algebra of standard differential operators and…
We consider systems of linear differential and difference equations \begin{eqnarray*} \partial Y(x) =A(x)Y(x), \sigma Y(x) =B(x)Y(x) \end{eqnarray*} with $\partial = \frac{d}{dx}$, $\sigma$ a shift operator $\sigma(x) = x+a$, $q$-dilation…
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
We study the stability of the differential process of Rochberg and Weiss associated to an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of K\"othe function spaces we complete…
We characterize interpolating sequences for pairs of reproducing kernels $(s, \ell)$, where $s$ is a complete Pick factor of $\ell.$ This answers a question of Aleman, Hartz, McCarthy and Richter.
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
Here we define Rarita-Schwinger operators on cylinders and construct their fundamental solutions. Further the fundamental solutions to the cylindrical Rarita-Schwinger type operators are achieved by applying translation groups. In turn, a…
Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$…