Related papers: From sphere packing to Fourier interpolation
We give a concise direct proof of the orthogonality of interpolation Macdonald polynomials with respect to the Fourier pairing and briefly discuss some immediate applications of this orthogonality, such as the symmetry of the Fourier…
Using factorisation and Arov-Krein inequality results, we derive important inequalities (in terms of $S$-nodes) in interpolation problems.
A dimensional interpolation between the free energy and conformal anomaly on spheres is derived for free scalar and spinor fields on the basis of standard field theory. The regularisation used is an extension of one by Candelas and…
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.
Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in \cite{LSX}. The main results consist of a new derivation of the Gaussian type cubature for the…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
The sphere packing problem is an old puzzle. We consider packings with m spheres in the unit cell (m-periodic packings). For the case m = 1 (lattice packings), Voronoi proved there are finitely many inequivalent local optima and presented…
We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…
Let $K$ be a totally real number field of degree $n \geq 2$. The inverse different of $K$ gives rise to a lattice in $\mathbb{R}^n$. We prove that the space of Schwartz Fourier eigenfunctions on $\mathbb{R}^n$ which vanish on the…
Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we…
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…
We represent the Fourier form of the dressing method, which is effective for construction of multidimensional integral-differential equations together with their solutions. Example of integrable (but non-physical) expansion of Intermediate…
How should you choose a good set of (say) 48 planes in four dimensions? More generally, how do you find packings in Grassmannian spaces? In this article I give a brief introduction to the work that I have been doing on this problem in…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…
We give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications including optics and atmospheric sciences. In this paper, we…
Building on recent advances in studying the co-homological properties of Feynman integrals, we apply intersection theory to the computation of Fourier integrals. We discuss applications pertinent to gravitational bremsstrahlung and deep…
In this paper we introduce new modules over the ring of ponderation functions, so we recover old results in harmonic analysis from the side of ring theory. Moreover, we prove that Laplace transform, Fourier transform and Hankel transform…
A new approach for solving the optical inverse problem of quantitative photoacoustic tomography is introduced, which interpolates between the well-known diffusion approximation and a radiative transfer equation based model. The proposed…