The kaehlerian structures and reproducing kernels

• Autorzy: Anna Krok , Tomasz Mazur
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

kaehlerian manifold; kaehlerian potential; positive definite function; Bergman function; reproducing kernel

Kategorie tematyczne

• 58A32: Natural bundles

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 55
• Numer: 1
• Strony: 221-224

Daty

wydano

1991

otrzymano

1990-09-14

Twórcy

autor

Anna Krok

• Department of Mathematics, Technical University of Radom, Malczewskiego 29, 26-600 Radom, Poland

autor

Tomasz Mazur

• Department of Mathematics, Technical University of Radom, Malczewskiego 29, 26-600 Radom, Poland

Bibliografia

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