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Bulletin of the London Mathematical Society Advance Access originally published online on January 24, 2009
Bulletin of the London Mathematical Society 2009 41(1):117-123; doi:10.1112/blms/bdn109
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© 2009 London Mathematical Society

A Blaschke-type condition and its application to complex Jacobi matrices

A. Borichev

Université Aix-Marseille
39, rue Joliot-Curie
13453 Marseille
Cedex 13
France
borichev@cmi.univ-mrs.fr

L. Golinskii

Mathematics Division
Institute for Low Temperature Physics and Engineering
47 Lenin ave.
Kharkov 61103
Ukraine
leonid.golinskii@gmail.com

S. Kupin

Université Aix-Marseille
39, rue Joliot-Curie
13453 Marseille
Cedex 13
France

Received 3 January 2008. Revision received 11 September 2008.

We obtain a Blaschke-type necessary condition on zeros of analytic functions on the unit disc with different types of exponential growth at the boundary. These conditions are used to prove Lieb–Thirring-type inequalities for the eigenvalues of complex Jacobi matrices.

2000 Mathematics Subject Classification 30C15 (primary), 47B36 (secondary).

The first author was partially supported by ANR DYNOP grant. The third author was partially supported by ANR AHPI grant.


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