Vol. 74, No. 1, 1978

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Moment sequences obtained from restricted powers

Rodney V. Nillsen

Vol. 74 (1978), No. 1, 183–190
Abstract

Let (mn)n=1 be an increasing divergent sequence of positive numbers. Then we are interested in characterising those sequences (αn)n=1 for which αn = 01xmnf(x)dx for n = 1,2, and some f L2([0,1)). It is shown that if (mn)n=1 diverges sufficiently rapidly, then n1|αn|2 < if and only if an = √mn-- 01xmnf(x)dx for n = 1,2, and some f L2([0,1)). It is also shown that if (mn)n=1 is a lacunary sequence of integers then the Hilbert subspace of L2([0,1)) generated by the functions xmn (n = 1,2,) has a reproducing kernel.

Mathematical Subject Classification 2000
Primary: 44A50, 44A50
Secondary: 46E20
Milestones
Received: 18 March 1977
Revised: 15 June 1977
Published: 1 January 1978
Authors
Rodney V. Nillsen