Geodesic
Spectral properties of holomorphic automorphism with fixed point
Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 25-30

Voir la notice de l'article provenant de la source Cambridge University Press

The Hilbert space methods in the theory of biholomorphic mappings were applied and developed by S. Bergman [1, 2]. In this approach the central role is played by the Hilbert space L2H(D) consisting of all functions which are square integrable and holomorphic in a domain D ⊂ CN. A biholomorphic mapping φ:D ⃗ G induces the unitary mapping Uφ:L2H(G) ⃗ L2H(D) defined by the formulaHere ∂φ/∂z denotes the complex Jacobian of φ. The mapping Uφ is useful, since it permits to replace a problem for D by a problem for its biholomorphic image G (see for example [11], [13]). When φ is an automorphism of D we obtain a unitary operator Uφ on L2H(D). 
Mazur, T.; Skwarczyński, M. Spectral properties of holomorphic automorphism with fixed point. Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 25-30. doi: 10.1017/S0017089500006297
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