Abstract We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) sparse exponential sums. Our algorithm uses the AAA rational approximation discrete Fourier transform given equidistant signal values. show that ESPIRA can be interpreted as matrix pencil (MPM) applied to Loewner matrices. These matrices are closely connected with Hankel usu...

The literature on Dedekind sums is vast. In this expository paper we show that there is a common thread to many generalizations of Dedekind sums, namely through the study of lattice point enumeration of rational poly-topes. In particular, there are some natural finite Fourier series which we call Fourier-Dedekind sums, and which form the building blocks of the number of partitions of an integer...

‎the main purpose of this note is to establish some bounds in poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎some results related to random sums of independent geometric distributed random variables are also investigated.

We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of ...

We construct an approximation of the free space Green’s function for the Helmholtz equation that splits the application of this operator between the spatial and the Fourier domains, as in Ewald’s method for evaluating lattice sums. In the spatial domain we convolve with a sum of decaying Gaussians with positive coefficients and, in the Fourier domain, we multiply by a band-limited kernel. As a ...

We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasipolynomial of a rational simplex, Math. Comp. 75 (2006), 1449– 1466]. By well-known decompositions, it is sufficient to consider the case of affine cones s+c, where s is an arbitrary real vertex and c is a rational polyhed...