Related papers: Sampling and interpolation for the discrete Hilber…
We present a general approach to derive sampling theorems on locally compact groups from oscillation estimates. We focus on the ${\rm L}^2$-stability of the sampling operator by using notions from frame theory. This approach yields…
A \Riesz-basis sequence for $L_2[-\pi,\pi]$ is a strictly increasing sequence $X:=(x_j)_{j\in\mathbb{Z}}$ in $\mathbb{R}$ such that the set of functions $\left(e^{-ix_j(\cdot)}\right)_{j\in\mathbb{Z}}$ is a Riesz basis for $L_2[-\pi,\pi]$.…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a standard assumption formulated in terms of…
In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this…
This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert…
We study multiple sampling and interpolation problems with unbounded multiplicities in the weighted Bergman space, both in the hilbertian case p = 2 and the uniform case p = +$\infty$.
Aim of this paper is to prove the second order differentiation formula along geodesics in compact $RCD^*(K,N)$ spaces with $N<\infty$. This formula is new even in the context of Alexandrov spaces. We establish this result by showing that…
We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the…
The paper is devoted to the construction of an optimal interpolation formula in $K_2(P_2)$ Hilbert space. Here the interpolation formula consists of a linear combination $\sum_{\beta=0}^NC_{\beta}(z)\varphi(x_\beta)$ of given values of a…
We prove an abstract interpolation theorem which interpolates the (r,2)-summing and (s,2)-mixing norm of a fixed operator in the image and the range space. Combined with interpolation formulas for spaces of operators we obtain as an…
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.
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…
The Zak transform on $\mathbb{R}^d$ is an important tool in condensed matter physics, signal processing, time-frequency analysis, and harmonic analysis in general. This article introduces a generalization of the Zak transform to a class of…
We formalize a technique for embedding Riemann sufraces properly into \C^2, and we generalize all known embedding results to allow interpolation on prescribed discrete sequences.
Let k be an algebraically closed field of characteristic p>2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the symplectic group over k in terms of cap-curl diagrams under…
We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions…
Weighted discrete Hilbert transforms $(a_n)_n \mapsto \sum_n a_n v_n/(z-\gamma_n)$ from $\ell^2_v$ to a weighted $L^2$ space are studied, with $\Gamma=(\gamma_n)$ a sequence of distinct points in the complex plane and $v=(v_n)$ a…
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…