Related papers: $L^2-$interpolation with error and size of spectra

Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The…

We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process…

We prove an interpolation formula for the values of certain $p$-adic Rankin--Selberg $L$-functions associated to non-ordinary modular forms.

Let $N$ be the Heisenberg group. We consider left-invariant multiplicity free subspaces of $L^2(N)$. We prove a necessary and sufficient density condition in order that such subspaces possess the interpolation property with respect to a…

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 functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…

We give a characterization of interpolating sequences for bounded analytic functions on the bidisk.

One classical measure of the quality of an interpolating function is its Lipschitz constant. In this paper we consider interpolants with additional smoothness requirements, in particular that their derivatives be Lipschitz. We show that…

Schwarz's Lemma leads to a natural interpolation problem for analytic functions from the disc into itself. The corresponding interpolating sequences are geometrically described in terms of a certain hyperbolic density.

We deal with the electromagnetic waves propagation in the harmonic regime. We derive the Foldy-Lax approximation of the scattered fields generated by a cluster of small conductive inhomogeneities arbitrarily distributed in a bounded domain…

The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable to the wavelength of the incident radiation. The DDA can be extended to targets…

Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.

We prove that a suitably adjusted version of Peter Jones' formula for interpolation by bounded holomorphic functions gives a sharp upper bound for what is known as the constant of interpolation. We show how this leads to precise and…

Let (X j , d j , $\mu$ j), j = 0, 1,. .. , m be metric measure spaces. Given 0 < p $\kappa$ $\le$ $\infty$ for $\kappa$ = 1,. .. , m and an analytic family of multilinear operators T z : L p 1 (X 1) x $\bullet$ $\bullet$ $\bullet$ L p m (X…

This paper addresses the problem of an efficient predictive density estimation for the density $q(\|y-\theta\|^2)$ of $Y$ based on $X \sim p(\|x-\theta\|^2)$ for $y, x, \theta \in \mathbb{R}^d$. The chosen criteria are integrated $L_1$ loss…

We discuss a method to estimate the measure of a compact set which is approximated using the Hausdorff distance by a sequence of compact sets. We do this by considering corresponding fattenings of the sequence of compact sets and showing…

Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work, we show a priori rates of convergence of this…

Knowledge of the scatter in the mass-observable relation is a key ingredient for a cosmological analysis based on galaxy clusters in a photometric survey. In this paper we aim to quantify the capability of the correlation function of galaxy…

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.

We compute the K-functional related to some couple of spaces as small or classical Lebesgue space or Lorentz-Marcinkiewicz spaces completing the results of the previous works of the authors. This computation allows to determine the…