Related papers: Multiple sampling and interpolation in the classic…
In this note, we investigate some topological properties of probabilistic modular spaces.
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
This chapter surveys some of the main results on interpolation in several of the most prominent families of non-classical logics. Special attention is given to the distinction between the two most commonly studied variants of…
Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein…
We investigate the space of simplices in Euclidean Space
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
We study deformation spaces using multi-centered dilatations. Interpolating Fulton simple deformation space and Rost asymmetric double deformation space, we introduce (asymmetric) deformation spaces attached to chains of immersions of…
An algebraic approach is presented for the valuative interpolation problem, which recovers and generalizes prior characterizations known in the complex analytic setting by the authors. We use the asymptotic Samuel function to give the…
We characterize the region of meromorphic continuation of an analytic function $f$ in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of $f$. The rational approximants have a…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
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 discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of…
We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber…
In this work, we show that the complex interpolation space is the same by the two methods.
We propose two possible definitions for the notion of a sampling sequence (or set) for Hardy spaces of the disk. The first one is inspired by recent work of Bruna, Nicolau, and \O yma about interpolating sequences in the same spaces, and it…
In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the…
Multiphoton interference is an essential phenomenon at the very heart not only of fundamental quantum optics and applications in quantum information processing and sensing but also of demonstrations of quantum computational supremacy in…