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

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In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces ( b ) , where b is in the unit ball of H ( + ) . 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

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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 1 , where Δ 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.

Embedding theorems for Müntz spaces

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2011)

Annales de l’institut Fourier

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We discuss boundedness and compactness properties of the embedding M Λ 1 L 1 ( μ ) , where M Λ 1 is the closed linear span of the monomials x λ n in L 1 ( [ 0 , 1 ] ) and μ is a finite positive Borel measure on the interval [ 0 , 1 ] . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences Λ . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators...