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Bulletin of the London Mathematical Society Advance Access originally published online on September 30, 2009
Bulletin of the London Mathematical Society 2009 41(5):903-915; doi:10.1112/blms/bdp068
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© 2009 London Mathematical Society

Eigenvalue decay of operators on harmonic function spaces

Oscar F. Bandtlow

School of Mathematical Sciences
Queen Mary University of London
London
E1 4NS
United Kingdom

Cho-Ho Chu

School of Mathematical Sciences
Queen Mary University of London
London
E1 4NS
United Kingdom
c.chu@qmul.ac.uk

Received 9 March 2008. Revision received 5 March 2009.

Let {Omega} be an open set in Rd (d > 1) and let h({Omega}) be the Fréchet space of harmonic functions on {Omega}. Given a bounded linear operator L : h ({Omega}) -> h({Omega}), we show that its eigenvalues {lambda}n, arranged in decreasing order and counting multiplicities, satisfy |{lambda}n| ≤ K exp(–cn1/(d–1)), where K and c are two explicitly computable positive constants.

2000 Mathematics Subject Classification 47B38 (primary), 47B07, 47B06, 46E10, 31B05 (secondary).


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