Vol. 49, No. 2, 1973

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On the Lu Qi-Keng conjecture and the Bergman representative domains

Shozo Matsuura

Vol. 49 (1973), No. 2, 407–416

The main purpose of this paper is to give the affirmative solution for the Lu Qi-Keng conjecture in the case of bounded complete circular domains.

Some results are that Bell’s proposition, which is related to the evaluation about the Bergman kernel functions of homogeneous complete circular domains, is extended to the case of bounded complete circular domains and that the Bergman representative functions with respect to z0(0) of any bounded and any homogeneous bounded complete circular domain with center at the origin are biholomorphic and isomorphic (biholomorphic in the narrow sense), respectively.

Mathematical Subject Classification
Primary: 32H05
Secondary: 32H10
Received: 23 December 1971
Published: 1 December 1973
Shozo Matsuura