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On a gap series of Mark Kac

Katusi Fukuyama (1999)

Colloquium Mathematicae

Mark Kac gave an example of a function f on the unit interval such that f cannot be written as f(t)=g(2t)-g(t) with an integrable function g, but the limiting variance of n - 1 / 2 k = 0 n - 1 f ( 2 k t ) vanishes. It is proved that there is no measurable g such that f(t)=g(2t)-g(t). It is also proved that there is a non-measurable g which satisfies this equality.

On a Szegö's theorem of orthogonal polynomials.

Jesús Sánchez Dehesa (1979)

Revista Matemática Hispanoamericana

It is found that the asymptotical density of zeros of a system of orthogonal polynomials whose weight function belongs to a wide class of distribution functions has the expression ρ(x) = π-1 (1 - x2)-1/2. This result is shown in two completely different ways: (1) from a Szegö theorem and (2) from a Geronimus theorem and a finding recently obtained by the author in a context of Jacobi matrices.

On a Theorem of Ingham.

S. Jaffard, M. Tucsnak, E. Zuazua (1997)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

On | A , δ | k -summability of orthogonal series

Xhevat Z. Krasniqi (2012)

Mathematica Bohemica

In the paper, we prove two theorems on | A , δ | k summability, 1 k 2 , of orthogonal series. Several known and new results are also deduced as corollaries of the main results.

On analytic rapidly decreasing functions of a real variable

Gianfranco Cimmino (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Condizione necessaria e sufficiente affinché una funzione rapidamente decrescente di variabile reale sia uniformemente analitica è che per i suoi coefficienti γ 0 , γ 1 , di Fourier-Hermite riesca γ m = 0 ( e m t ) per t > 0 abbastanza piccolo.

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