Related papers: Differential processes generated by two interpolat…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Continuation refers to the operation by which the cumulative distribution function of a discontinuous random vector is made continuous through multilinear interpolation. The copula that results from the application of this technique to the…
We classify and construct $SL(n,\mathbb{R})$-intertwining differential operators $\mathcal{D}$ from a line bundle to a vector bundle over the real projective space $\mathbb{RP}^{n-1}$ by the F-method. This generalizes a classical result of…
In this short note, we investigate the relationship between so-called regular families of cardinal interpolators and multiresolution analyses. We focus our studies on examples of regular families of cardinal interpolators whose Fourier…
We continue the work of S. Tikhonov, E. Liflyand, B. Booton, and others, proving the equivalence of L(p,q)-norms of general monotone functions and of their Fourier transforms. The main tool in this work is the interpolation properties of…
We distinguish a class of random point processes which we call Giambelli compatible point processes. Our definition was partly inspired by determinantal identities for averages of products and ratios of characteristic polynomials for random…
We study various properties of $f$-divergences and Csisz\'ar indices between two probability distributions in very general setups for the convex function $f$ and for the probability distributions. We establish general structural properties…
The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is superintegrable and its symmetry generators…
We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.
The second part of our work on operator synthesis deals with individual operator synthesis of elements in some tensor products, in particular in Varopoulos algebras, and its connection with linear operator equations. Using a developed…
This paper studies the cardinal interpolation operators associated with the general multiquadrics, $\phi_{\alpha,c}(x) = (\|x\|^2+c^2)^\alpha$, $x\in\mathbb{R}^d$. These operators take the form $$\mathscr{I}_{\alpha,c}\mathbf{y}(x) =…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
Interpolation-based techniques become popular in recent years, as they can improve the scalability of existing verification techniques due to their inherent modularity and local reasoning capabilities. Synthesizing Craig interpolants is the…
In this article we study differential symmetry breaking operators between principal series representations induced from minimal parabolic subgroups for the pair $(\operatorname{GL}_{n+1}(\mathbb{R}),\operatorname{GL}_n(\mathbb{R}))$. Using…
We investigate different geometrical properties of the inhomogeneous Poisson point process $\Lambda_{\mu}$ associated to a positive, locally finite, $\sigma$-finite measure $\mu$ on the unit disk. In particular, we characterize the…
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…
We construct Rankin-Cohen type differential operators on Hermitian modular forms of signature $(n,n)$. The bilinear differential operators given here specialize to the original Rankin-Cohen operators in the case $n=1$, and more generally…
We discuss a general scheme for a construction of linear conformally invariant differential operators from curved Casimir operators; we then explicitly carry this out for several examples. Apart from demonstrating the efficacy of the…
Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators and the method of boundary equations, we describe Dirichlet…
We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…