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Vanishing l1-sums of the Poisson kernel, and sums with positive coefficients

Published online by Cambridge University Press:  20 January 2009

F. F. Bonsall  and
D. Walsh
F. F. Bonsall
Affiliation:
School of MathematicsUniversity of LeedsLeeds LS2 9JTEngland
D. Walsh
Affiliation:
Department of MathematicsMaynooth CollegeCo. KildareIreland
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For z in D and ζ in ∂D, we denote by pz(ζ) the Poisson kernel (1 − │z│2)│1 − ζ−2 for the open unit disc D. We ask for what countable sets {an:n∈ℕ} of points of D there exist complex numbers λn with

by which we mean that the series converges to zero in the norm of L1(∂D).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 3 , October 1989 , pp. 431 - 447
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

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