Related papers: Approximation properties of the double Fourier sph…
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability estimates that grant spectral convergence of the…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
We present a super-high-efficiency approximate computing scheme for series sum and discrete Fourier transform. The summation of a series sum or a discrete Fourier transform is approximated by summing over part of the terms multiplied by…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
Given values of a piecewise smooth function $f$ on a square grid within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. Standard approximation techniques achieve reduced approximation orders near the boundary of…
Every stable 4-sphere is identified with the double branched covering space of a trivial surface-knot space. As a result of Wall, it is known that any two orthogonal bases of every stable 4-sphere are transformed into each other by an…
Approximative properties of linear summation methods of Fourier series are considered in the Orlicz type spaces ${\mathcal S}_{M}$. In particular, in terms of approximations by such methods, constructive characteristics are obtained for…
Finite Sample Smeariness (FSS) has been recently discovered. It means that the distribution of sample Fr\'echet means of underlying rather unsuspicious random variables can behave as if it were smeary for quite large regimes of finite…
We show that for every complete Riemannian surface $M$ diffeomorphic to a sphere with $k \geq 0$ holes there exists a Morse function $f:M \rightarrow \mathbb{R}$, which is constant on each connected component of the boundary of $M$ and has…
A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…
In this paper, we propose a unified theoretical and practical spherical approximation framework for functional inverse problems on the hypersphere. More specifically, we consider recovering spherical fields directly in the continuous domain…
Several problems on Fourier series and trigonometric approximation on a hexagon and a triangle are studied. The results include Abel and Ces\`aro summability of Fourier series, degree of approximation and best approximation by trigonometric…
We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…
Two methods for fast Fourier transforms are used in a quantum context. The first method is for systems with dimension of the Hilbert space $D=d^n$ with $d$ an odd integer, and is inspired by the Cooley-Tukey formalism. The `large Fourier…
We consider fast, provably accurate algorithms for approximating functions on the $d$-dimensional torus, $f: \mathbb{ T }^d \rightarrow \mathbb{C}$, that are sparse (or compressible) in the Fourier basis. In particular, suppose that the…
This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d. Our Fourier duality applies to the resulting probability…
We resolve three longstanding questions related to the large scale geometry of the group of Hamiltonian diffeomorphisms of the two-sphere, equipped with Hofer's metric. Namely: (1) we resolve the Kapovich-Polterovich question by showing…
Given cell-average data values of a piecewise smooth bivariate function $f$ within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. We are interested in an explicit and global (smooth) approach. Bivariate…
The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental…