Geodesic
Unconditional Exponential Bases in Bergman Spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 88-100.

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It is proved that unconditional exponential bases cannot be constructed in the Bergman space $B_2(D)$ in the case when $D$ is a bounded convex domain in the plane such that at least at one point of its boundary the curvature exists and is different from zero. 
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K. P. Isaev; R. S. Yulmukhametov. Unconditional Exponential Bases in Bergman Spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 88-100. http://geodesic.mathdoc.fr/item/TM_2006_253_a7/

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