Related papers: Nevanlinna-Pick interpolation on distinguished var…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
This is an expanded version of the two papers "Interpolation of Varieties of Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general…
In this article, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets related to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation…
We develop Nevanlinna's theory for a class of holomorphic maps when the source is a disc. Such maps appear in the theory of foliations by Riemann Surfaces.
The paper studies the interpolation properties of net spaces $N_{p,q}(M)$, when $M$ is the set of dyadic cubes in $\mathbb{R}^n$, and also when $M$ is the family of all cubes with parallel faces to the coordinate axes in $\mathbb{R}^n$. It…
We extend the classical theory of variational interpolating splines to the case of compact Riemannian manifolds. Our consideration includes in particular such problems as interpolation of a function by its values on a discrete set of points…
It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general points. We prove a generalization of this to higher dimensional varieties, showing that smooth varieties of minimal degree can be interpolated…
Given a principally polarized abelian variety $(A,\Theta)$, we give a characterization of all elliptic curves that lie on $A$ in terms of intersection numbers of divisor classes in its N\'eron-Severi group.
We prove a boundedness-theorem for families of abelian varieties with real multiplication. More generally, we study curves in Hilbert modular varieties from the point of view of the Green Griffiths-Lang conjecture claiming that entire…
Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate…
This paper describes a paving by affines for regular nilpotent Hessenberg varieties in all Lie types, namely a kind of cell decomposition that can be used to compute homology despite its weak closure conditions. Precup recently proved a…
The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting…
Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference…
The Prym variety for a branched double covering of a nonsingular projective curve is defined as a polarized abelian variety. We prove that any double covering of an elliptic curve which has more than $4$ branch points is recovered from its…
We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…
We define a special matrix multiplication among a special subset of $2N\x 2N$ matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative…
We show that the Hardy space on the unit disk is the only non-trivial irreducible reproducing kernel Hilbert space which satisfies the complete Nevanlinna-Pick property and hyponormality of all multiplication operators.
We introduce a Grassmannian structure for a class of quotient Hilbert modules and attack the polydisc version of Arveson-Douglas conjecture associated to distinguished varieties. More interestingly, we obtain an operator-theoretic…
Van der Waals interactions are ubiquitous and they play an important role for the stability of materials. Current understanding of this type of coupling is based on linear response theory, while optical nonlinearities are rarely considered…
$p$-Adic divergence and gradient operators are constructed giving rise to $p$-adic vertex Laplacian operators used by Z\'u\~niga in order to study Turing patterns on graphs, as well as their edge Laplacian counterparts. It is shown that the…