Real Analysis Exchange

An Application of the Hardy-Littlewood Tauberian Theorem to Harmonic Expansion of a Complex Measure on the Sphere

Yifei Pan and Mei Wang

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Abstract

We apply Hardy-Littlewood's Tauberian theorem to obtain an estimate on the harmonic expansion of a complex measure on the unit sphere, using a monotonicity property for positive harmonic functions.

Article information

Source
Real Anal. Exchange Volume 35, Number 2 (2009), 517-524.

Dates
First available in Project Euclid: 22 September 2010

Permanent link to this document
http://projecteuclid.org/euclid.rae/1285160550

Mathematical Reviews number (MathSciNet)
MR2683617

Zentralblatt MATH identifier
05904838

Subjects
Primary: 40E05: Tauberian theorems, general 33C55: Spherical harmonics
Secondary: 30C85: Capacity and harmonic measure in the complex plane [See also 31A15]

Keywords
Tauberian theorem spherical harmonics complex measures zonal functions

Citation

Pan, Yifei; Wang, Mei. An Application of the Hardy-Littlewood Tauberian Theorem to Harmonic Expansion of a Complex Measure on the Sphere. Real Anal. Exchange 35 (2009), no. 2, 517--524. http://projecteuclid.org/euclid.rae/1285160550.


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References

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