Sets of $k$-recurrence but not $(k+1)$-recurrence

Nikos Frantzikinakis; Emmanuel Lesigne; Máté Wierdl

Displaying similar documents to “Sets of $k$ -recurrence but not $(k + 1)$ -recurrence”

Integral representation of the $n$ -th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel

Emmanuel Fricain, Javad Mashreghi (2008)

Annales de l’institut Fourier

Similarity:

In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces $ℋ (b)$ , where $b$ is in the unit ball of $H^{\infty} (ℂ_{+})$ . In particular, we generalize a result of Ahern–Clark obtained for functions of the model spaces $K_{b}$ , where $b$ is an inner function. Using hypergeometric series, we obtain a nontrivial formula of combinatorics for sums of binomial coefficients. Then we apply this formula to show the norm convergence of reproducing kernel...

On a binary recurrent sequence of polynomials

Reinhardt Euler, Luis H. Gallardo, Florian Luca (2014)

Communications in Mathematics

Similarity:

In this paper, we study the properties of the sequence of polynomials given by $g_{0} = 0, g_{1} = 1$ , $g_{n + 1} = g_{n} + Δ g_{n - 1}$ for $n \geq 1$ , where $Δ \in 𝔽_{q} [t]$ is non-constant and the characteristic of $𝔽_{q}$ is $2$ . This complements some results from R. Euler, L.H. Gallardo: On explicit formulae and linear recurrent sequences, Acta Math. Univ. Comenianae, 80 (2011) 213-219.