Related papers: Derivation of vector-valued complex interpolation …
The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
We simplify and give an alternative proof of hypoellipticity for generalizations of the singular sum of squares of complex vector fields studied by Kohn, with an appendix by Derridj and Tartakoff, in the Annals of Mathematics, vol. 162 no.…
In this paper we present a criteria to obtain interpolations formulas in terms of the sequence $\left(\{T_n(f)(Nm)\}\}_{m\in\mathbb{Z}}\right)_{n=1}^N$, where $f$ are functions whose Fourier transform is supported in $[-1/2,1/2]$, and $T_n$…
The use of interpolants in verification is gaining more and more importance. Since theories used in applications are usually obtained as (disjoint) combinations of simpler theories, it is important to modularly re-use interpolation…
The usual univariate interpolation problem of finding a monic polynomial f of degree n that interpolates n given values is well understood. This paper studies a variant where f is required to be composite, say, a composition of two…
The present paper studies the existence of valuative interpolation on the local ring of an irreducible analytic subvariety at singular points. We firstly develop the concepts and methods of Zhou weights and Tian functions near singular…
We present the real interpolation with variable exponent and we prove the basic properties in analogy to the classical real interpolation. More precisely, we prove that under some additional conditions, this method can be reduced to the…
In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in…
We construct coordinates on conjugacy classes of traceless complex matrices with simple spectrum that diagonalize the non-periodic Toda vector field. By this we mean that the coordinates, defined on an open and dense neighborhood of any…
We study the complex interpolation and derivation process induced by a family of Orlicz sequence spaces. We present a concrete example of interpolation family of three spaces inducing a centralizer that cannot be obtained from complex…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
One frequently needs to interpolate or approximate gradients on simplicial meshes. Unfortunately, there are very few explicit mathematical results governing the interpolation or approximation of vector-valued functions on Delaunay meshes in…
We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler…
The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.
We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the…
The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from…
This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…
We study complex interpolation of variable Triebel-Lizorkin spaces, especially we present the complex interpolation of $F_{p(\cdot),q}^{\alpha }$ and $F_{p(\cdot ),p(\cdot )}^{\alpha (\cdot )}$ spaces. Also, some limiting cases are given.