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Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)

100%

Shukurov A.

Colloquium Mathematicum

2014

tom 137

nr 2

297-298

It is well known that if φ(t) ≡ t, then the system ${φⁿ(t)}_{n=0}^{∞}$ is not a Schauder basis in L₂[0,1]. It is natural to ask whether there is a function φ for which the power system ${φⁿ(t)}_{n=0}^{∞}$ is a basis in some Lebesgue space $L_{p}$. The aim of this short note is to show that the answer to this question is negative.

Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces

100%

Shukurov A.

Colloquium Mathematicum

2012

tom 127

nr 1

105-109

A necessary condition for Kostyuchenko type systems and system of powers to be a basis in $L_{p}$ (1 ≤ p < +∞) spaces is obtained. In particular, we find a necessary condition for a Kostyuchenko system to be a basis in $L_{p}$ (1 ≤ p < +∞).

Ograniczanie wyników

2 Colloquium Mathematicum

2 Shukurov A.

1 2014

1 2012

Wyniki wyszukiwania

Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)

Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces