相关论文: Hook Interpolations

We discuss a possible noncommutative generalization of the notion of an equivariant vector bundle. Let $A$ be a $\mathbb{K}$-algebra, $M$ a left $A$-module, $H$ a Hopf $\mathbb{K}$-algebra, $\delta:A\to H\otimes A:=H\otimes_{\mathbb{K}} A$…

Exterior powers play important roles in persistent homology in computational geometry. In the present paper we study the problem of extracting the $K$ longest intervals of the exterior-power layers of a tame persistence module. We prove a…

Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate…

Classical Gon\v{c}arov polynomials are polynomials which interpolate derivatives. Delta Gon\v{c}arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental…

A natural interpolation problem in the cone of positive harmonic functions is considered and the corresponding interpolating sequences are geometrically described.

In this survey article some classical results concerning real interpolation between Hardy spaces are briefly presented and then it is explained how those results can be used to establish Yano-type extrapolation theorems for Hardy spaces.…

This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…

In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence…

This paper contains the first knot polynomials which can distinguish the orientations of classical knots and which make no excplicit use of the knot group. But they make extensive use of the meridian and of the longitude in a geometric way.…

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…

A point particle approximation to the classical dynamics of well separated vortices of the abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized field theory (a Klein-Gordon/Proca…

In this work, we obtain the Helmholtz decomposition for vector fields in Morrey, Zorko, and block spaces over bounded or exterior $C^{1}$ domains. Generally speaking, our proofs rely on a careful interplay of localization, flattening, and…

The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…

The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the $\delta$ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the…

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…

In this work, we study the Hermite interpolation on $n$-dimensional non-equally spaced, rectilinear grids over a field $\Bbbk $ of characteristic zero, given the values of the function at each point of the grid and the partial derivatives…

An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. As a prototype of classical monodromy with azimuthal symmetry, we consider a linear molecule interacting with external fields and…

We consider Gaussian fields of real symmetric, complex Hermitian or quaternionic Hermitian matrices over an electrical network, and describe how the isomorphisms between these fields and random walks give rise to topological expansions…

Interpolation Theory gives techniques for constructing spaces from two initial Banach spaces. We provide several conditions under which the restriction of a holomorphic map $f:X_0+X_1 \rightarrow Y_0+Y_1$ to the interpolated spaces (using…

We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of…