Vol. 50, No. 2, 1974

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ISSN: 0030-8730
Polynomials and Hausdorff matrices

Philip C. Tonne

Vol. 50 (1974), No. 2, 613–615
Abstract

If f is a function from the rational numbers in [0,1] to the complex plane and c is a complex sequence, then the Hausdorff matrix H(c) for c and a sequence L(f,c) are defined:

        (n )n∑−p     (n − p)      (n )
H(c)np =  p    (− 1)q  q   cp+q =  p Δn −pcp
q=0

         ∑n
L(f,c)n =    H(c)npf(p∕n).
p=0

Theorem. If f is a function from the rationals in [0,1] to the plane and L(f,c) converges for each complex sequence c, then f is a subset (contraction) of a polynomial.

Mathematical Subject Classification 2000
Primary: 41A05
Milestones
Received: 12 October 1972
Revised: 26 February 1973
Published: 1 February 1974
Authors
Philip C. Tonne