The kaehlerian structures and reproducing kernels

Anna Krok; Tomasz Mazur

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 221-224
  • ISSN: 0066-2216

Abstract

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It is shown that one can define a Hilbert space structure over a kaehlerian manifold with global potential in a natural way.

How to cite

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Anna Krok, and Tomasz Mazur. "The kaehlerian structures and reproducing kernels." Annales Polonici Mathematici 55.1 (1991): 221-224. <http://eudml.org/doc/262417>.

@article{AnnaKrok1991,
abstract = {It is shown that one can define a Hilbert space structure over a kaehlerian manifold with global potential in a natural way.},
author = {Anna Krok, Tomasz Mazur},
journal = {Annales Polonici Mathematici},
keywords = {kaehlerian manifold; kaehlerian potential; positive definite function; Bergman function; reproducing kernel; reproducing kernels; Hilbert space structure over a Kählerian manifold with global potential},
language = {eng},
number = {1},
pages = {221-224},
title = {The kaehlerian structures and reproducing kernels},
url = {http://eudml.org/doc/262417},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Anna Krok
AU - Tomasz Mazur
TI - The kaehlerian structures and reproducing kernels
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 221
EP - 224
AB - It is shown that one can define a Hilbert space structure over a kaehlerian manifold with global potential in a natural way.
LA - eng
KW - kaehlerian manifold; kaehlerian potential; positive definite function; Bergman function; reproducing kernel; reproducing kernels; Hilbert space structure over a Kählerian manifold with global potential
UR - http://eudml.org/doc/262417
ER -

References

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  1. [1] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1956), 337-404. Zbl0037.20701
  2. [2] S. Bergman, The Kernel Function and Conformal Mapping, 2nd ed., Math. Surveys 5, Amer. Math. Soc., 1970. Zbl0208.34302
  3. [3] S. Bergman, Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande, J. Reine Angew. Math. 169 (1933), 1-42. 
  4. [4] S. Chern, Complex Manifolds without Potential Theory, 2nd ed., Springer, 1978. Zbl0158.33002
  5. [5] W. Chojnacki, On some holomorphic dynamical systems, Quart. J. Math. Oxford Ser. (2) 39 (1988), 159-172. Zbl0667.47018
  6. [6] S. Janson, J. Peetre and R. Rochberg, Hankel forms and the Fock space, Rev. Mat. Iberoamericana 3 (1987), 61-138. Zbl0704.47022
  7. [7] S. Kobayashi, On the automorphism group of a homogeneous complex manifold, Proc. Amer. Math. Soc. 12 (3) (1961), 359-361. Zbl0101.14302
  8. [8] T. Mazur, Canonical isometry on weighted Bergman spaces, Pacific J. Math. 136 (2) (1989), 303-310. Zbl0677.46015
  9. [9] T. Mazur, On the complex manifolds of Bergman type, preprint. Zbl1064.32500
  10. [10] T. Mazur and M. Skwarczyński, Spectral properties of holomorphic automorphism with fixed point, Glasgow Math. J. 28 (1986), 25-30. Zbl0579.46017
  11. [11] W. Mlak, Introduction to Hilbert Space Theory, PWN, Warszawa 1991. Zbl0745.47001
  12. [12] M. Skwarczyński, Biholomorphic invariants related to the Bergman functions, Dissertationes Math. 173 (1980). Zbl0443.32014

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