Related papers: Beyond Superoscillation: General Theory of Approxi…
We derive upper bounds on the difference between the orthogonal projections of a smooth function $u$ onto two finite element spaces that are nearby, in the sense that the support of every shape function belonging to one but not both of the…
In bandit algorithms, the randomly time-varying adaptive experimental design makes it difficult to apply traditional limit theorems to off-policy evaluation of the treatment effect. Moreover, the normal approximation by the central limit…
We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields $a$ in the context of stochastic homogenization. The large-scale regularity of $a$-harmonic functions is…
We are interested in the cycles obtained by slicing at all heights random Boltzmann triangulations with a simple boundary. We establish a functional invariance principle for the lengths of these cycles, appropriately rescaled, as the size…
We study the nonconserved phase ordering dynamics of the d = 2, 3 random field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three di- mensions, reporting a crossover…
Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation.…
We introduce a new numerically stable method for constructing superoscillatory wave forms inan arbitrary number of dimensions. The method allows the construction of superoscillatory square-integrable functions that match any desired smooth…
This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as the sum of a function twice differentiable in the extended sense and a subdifferentially…
Stochastic processes are often represented through orthonormal series expansions, a framework originating in the classical works of Lo\`eve and Karhunen and widely used for simulation and numerical approximation. While truncation error in…
We provide sufficient density condition for a set of nonuniform samples to give rise to a set of sampling for multivariate bandlimited functions when the measurements consist of pointwise evaluations of a function and its first $k$…
$R$-limited functions are multivariate generalization of band-limited functions whose Fourier transforms are supported within a compact region $R\subset\mathbb{R}^{n}$. In this work, we generalize sampling and interpolation theorems for…
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…
We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of…
Peculiar velocities induce apparent line of sight displacements of galaxies in redshift space, distorting the pattern of clustering in the radial versus transverse directions. On large scales, the amplitude of the distortion yields a…
We study growth rates for strongly continuous semigroups. We prove that a growth rate for the resolvent on imaginary lines implies a corresponding growth rate for the semigroup if either the underlying space is a Hilbert space, or the…
In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…
In this paper we compute the spherical Fourier expansions coefficients for the restriction of the generalised Wendland functions from $d-$dimensional Euclidean space to the (d-1)-dimensional unit sphere. The development required to derive…
We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…
We focus on the evolution of curvature perturbation on superhorizon scales by adopting the spatial gradient expansion and show that the nonlinear theory, called the beyond $\delta N$-formalism as the next-leading order in the expansion. As…