Related papers: Perturbed interpolation formulae and applications
Given $E_0, E_1, F_0, F_1, E$ rearrangement invariant function spaces, $a_0$, $a_1$, $b_0$, $b_1$, $b$ slowly varying functions and $0< \theta_0<\theta_1<1$, we characterize the interpolation spaces $$(\overline{X}^{\mathcal…
We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized…
It has been shown that Paley-Wiener functions may be recovered from their values on a complete interpolating sequence. This paper explores the same phenomenon, and gives a sufficient condition on a function $\phi(x)$, called an…
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…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…
Limiting real interpolation method is applied to describe the behaviour of the Fourier coefficients of functions that belong to spaces which are "very close" to L2.
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
This paper investigates some univariate and bivariate constrained interpolation problems using rational quartic fractal interpolation functions, which has been submitted long back in a reputed journal and revised as per the journal…
Self-adjoint Dirac systems and subclasses of canonical systems, which generalize Dirac systems are studied. Explicit and global solutions of direct and inverse problems are obtained. A local Borg-Marchenko-type theorem, integral…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…
We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of Lorentz-Marcinkiewicz type and also for the approximation spaces generated by symmetric norming functions…
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
Bayesian inverse problems are an important application for probabilistic solvers of partial differential equations: when fully resolving numerical error is computationally infeasible, probabilistic solvers can be used to consistently model…
We systematically develop real Paley-Wiener theory for the Fourier transform on R^d for Schwartz functions, L^p-functions and distributions, in an elementary treatment based on the inversion theorem. As an application, we show how versions…
This paper investigates functional equations arising from perturbations of Cauchy differences. We study equations of the form \[ f(x+y)-f(x)-f(y)=B(x,y) \quad \text{or} \quad f(xy)-f(x)f(y) = B(x,y) \] where $B$ is a biadditive mapping, and…
A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron is deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains.…
In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As…
Several problems of trigonometric approximation on a hexagon and a triangle are studied using the discrete Fourier transform and orthogonal polynomials of two variables. A discrete Fourier analysis on the regular hexagon is developed in…
We give a characterization of complete interpolating sequences for the Fock spaces $\mathcal{F}^p_\varphi,\ 1\leq p<\infty$, where $\varphi(z)=\alpha\left(\log^+|z|\right)^2,\ \alpha>0$. Our results are {analogous} to the classical…