Related papers: Improved interpolation inequalities on the sphere
In the present paper optimal interpolation formulas are constructed in $W_2^{(m,m-1)}(0,1)$ space. Explicit formulas for coefficients of optimal interpolation formulas are obtained. Some numerical results are presented.
We prove Ehrhard's inequality using interpolation along the Ornstein-Uhlenbeck semi-group. We also provide an improved Jensen inequality for Gaussian variables that might be of independent interest.
In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.
This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an…
The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates when designing…
This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result,…
We obtain rigorous results concerning the evaluation of integrals on the two sphere using complex methods. It is shown that for regular as well as singular functions which admit poles, the integral can be reduced to the calculation of…
In this paper, we study the H\"older-type interpolation inequality and observability inequality from measurable sets in time for parabolic equations either with L^p unbounded potentials or with electric potentials. The parabolic equations…
We introduce a new method for testing departure from isotropy of points on a sphere based on an enhanced form of the two-point correlation function that we named 2pt+. This method uses information from the two extra variables that define…
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.
A field in a homogeneous medium can be amplified or enhanced by inserting closely located perfectly conducting inclusions into the medium. In this paper precise quantitative estimates for such enhancement are derived when the given field is…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations
This paper describes the analysis of Lagrange interpolation errors on tetrahedrons. In many textbooks, the error analysis of Lagrange interpolation is conducted under geometric assumptions such as shape regularity or the (generalized)…
Hermite spectral method plays an important role in the numerical simulation of various partial differential equations (PDEs) on unbounded domains. In this work, we study the superconvergence properties of Hermite spectral interpolation,…
Interpolation inequalities for $C^m$ functions allow to bound derivatives of intermediate order $0 < j<m$ by bounds for the derivatives of order $0$ and $m$. We review various interpolation inequalities for $L^p$-norms ($1 \le p \le…
In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate $C^1$ quadratic splines on…
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are sharp. All results are under the assumptions that the…
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the…