Related papers: Exponential bases on triangular domains
The classical Euler's problem on optimal configurations of elastic rod in the plane with fixed endpoints and tangents at the endpoints is considered. The global structure of the exponential mapping that parameterises extremal trajectories…
We show that discrete exponentials form a basis of discrete holomorphic functions. On a convex, the discrete polynomials form a basis as well.
We construct two new families of basis for finite field extensions. Basis in the first family, the so-called elliptic basis, are not quite normal basis, but they allow very fast Frobenius exponentiation while preserving sparse…
We introduce and study non-uniform expansions of real numbers, given by two non-integer bases.
We prove the existence of Riesz bases of exponentials of L^2(Omega), provided that Omega in R^d is a measurable set of finite and positive measure, not necessarily bounded, that satisfies a multi-tiling condition and an arithmetic property…
We give a moderately motivated exposition of exponentiable locales and the construction of exponentials in $\textsf{Loc}$, without assuming prior knowledge of exponential topological spaces or continuous posets.
In the 1990's exponential-type error bounds appeared in the theory of radial basis functions. This kind of error bounds is very powerful. However it only measures the difference between the approximant and approximand. Mathematicians and…
We investigate the existence of "generic derivations" in exponential fields. We show that exponential fields without additional compatibility conditions between derivation and exponentiation cannot support a generic derivation.
We give defining equations for function fields over finite fields with many rational places. They are obtained from composita of quadratic extensions of the rational function field.
In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can…
We consider \textit{additive spaces}, consisting of two intervals of unit length or two general probability measures on ${\mathbb R}^1$, positioned on the axes in ${\mathbb R}^2$, with a natural additive measure $\rho$. We study the…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
We obtain sufficient conditions for an exponential type entire function not to have zeros in the open lower half-plane. An exact inequality containing the real and imaginary parts of such functions and their derivatives restricted to the…
We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M…
We provide two new bounds on the number of visible points on exponential curves modulo a prime for all choices of primes. We also provide one new bound on the number of visible points on exponential curves modulo a prime for almost all…
Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in \cite{Akh} as direct generalization of the ordinary non-commutative $P$-exponent for 1-forms with values in matrices (i.e.…
We give an estimate of exponential sums over singular binary quintic forms in a characteristic-free form, based on the Waring decomposition of binary forms. This extends the method on our preceding result on the space of binary quartics to…
The aim of this paper is to propose a new method to construct exponential attractors for infinite dimensional dynamical systems in Banach spaces with explicit fractal dimension. The approach is established by combing the squeezing…
We show that the points that converge to infinity under iteration of the exponential map form a connected subset of the complex plane.
We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number of solutions of certain equations involving products and differences of sets in prime finite fields to give an explicit upper bound on trilinear…