It is shown that one can define a Hilbert space structure over a kaehlerian manifold with global potential in a natural way.
@article{bwmeta1.element.bwnjournal-article-apmv55z1p221bwm,
author = {Anna Krok and Tomasz Mazur},
title = {The kaehlerian structures and reproducing kernels},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {221-224},
zbl = {0770.46007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p221bwm}
}
Anna Krok; Tomasz Mazur. The kaehlerian structures and reproducing kernels. Annales Polonici Mathematici, Tome 55 (1991) pp. 221-224. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p221bwm/
[000] [1] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1956), 337-404. | Zbl 0037.20701
[001] [2] S. Bergman, The Kernel Function and Conformal Mapping, 2nd ed., Math. Surveys 5, Amer. Math. Soc., 1970. | Zbl 0208.34302
[002] [3] S. Bergman, Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande, J. Reine Angew. Math. 169 (1933), 1-42.
[003] [4] S. Chern, Complex Manifolds without Potential Theory, 2nd ed., Springer, 1978. | Zbl 0158.33002
[004] [5] W. Chojnacki, On some holomorphic dynamical systems, Quart. J. Math. Oxford Ser. (2) 39 (1988), 159-172. | Zbl 0667.47018
[005] [6] S. Janson, J. Peetre and R. Rochberg, Hankel forms and the Fock space, Rev. Mat. Iberoamericana 3 (1987), 61-138. | Zbl 0704.47022
[006] [7] S. Kobayashi, On the automorphism group of a homogeneous complex manifold, Proc. Amer. Math. Soc. 12 (3) (1961), 359-361. | Zbl 0101.14302
[007] [8] T. Mazur, Canonical isometry on weighted Bergman spaces, Pacific J. Math. 136 (2) (1989), 303-310. | Zbl 0677.46015
[008] [9] T. Mazur, On the complex manifolds of Bergman type, preprint. | Zbl 1064.32500
[009] [10] T. Mazur and M. Skwarczyński, Spectral properties of holomorphic automorphism with fixed point, Glasgow Math. J. 28 (1986), 25-30. | Zbl 0579.46017
[010] [11] W. Mlak, Introduction to Hilbert Space Theory, PWN, Warszawa 1991. | Zbl 0745.47001
[011] [12] M. Skwarczyński, Biholomorphic invariants related to the Bergman functions, Dissertationes Math. 173 (1980). | Zbl 0443.32014