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1998 | 70 | 1 | 109-115
Tytuł artykułu

The Bergman kernel functions of certain unbounded domains

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We compute the Bergman kernel functions of the unbounded domains $Ω_p = {(z',z) ∈ ℂ² : 𝕴z > p(z')}$, where $p(z') = |z'|^{α}/α$. It is also shown that these kernel functions have no zeros in $Ω_p$. We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.
Słowa kluczowe
Rocznik
Tom
70
Numer
1
Strony
109-115
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-12-29
poprawiono
1998-08-14
Twórcy
  • Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
Bibliografia
  • [BFS] H. P. Boas, S. Fu and E. J. Straube, The Bergman kernel function: Explicit formulas and zeros, Proc. Amer. Math. Soc. (to appear).
  • [BL] A. Bonami and N. Lohoué, Projecteurs de Bergman et Szegő pour une classe de domaines faiblement pseudo-convexes et estimations $L^p$, Compositio Math. 46 (1982), 159-226.
  • [BSY] H. P. Boas, E. J. Straube and J. Yu, Boundary limits of the Bergman kernel and metric, Michigan Math. J. 42 (1995), 449-462.
  • [D'A] J. P. D'Angelo, An explicit computation of the Bergman kernel function, J. Geom. Anal. 4 (1994), 23-34.
  • [D] K. P. Diaz, The Szegő kernel as a singular integral kernel on a family of weakly pseudoconvex domains, Trans. Amer. Math. Soc. 304 (1987), 147-170.
  • [DO] K. Diederich and T. Ohsawa, On the parameter dependence of solutions to the ∂̅-equation, Math. Ann. 289 (1991), 581-588.
  • [FH1] G. Francsics and N. Hanges, Explicit formulas for the Szegő kernel on certain weakly pseudoconvex domains, Proc. Amer. Math. Soc. 123 (1995), 3161-3168.
  • [FH2] G. Francsics and N. Hanges, The Bergman kernel of complex ovals and multivariable hypergeometric functions, J. Funct. Anal. 142 (1996), 494-510.
  • [FH3] G. Francsics and N. Hanges, Asymptotic behavior of the Bergman kernel and hypergeometric functions, in: Contemp. Math. (to appear).
  • [GS] P. C. Greiner and E. M. Stein, On the solvability of some differential operators of type $⎕_b$, Proc. Internat. Conf., (Cortona, 1976-1977), Scuola Norm. Sup. Pisa, 1978, 106-165.
  • [Han] N. Hanges, Explicit formulas for the Szegő kernel for some domains in $ℂ^2$, J. Funct. Anal. 88 (1990), 153-165.
  • [Has1] F. Haslinger, Szegő kernels of certain unbounded domains in $ℂ^2$, Rév. Rou- maine Math. Pures Appl. 39 (1994), 914-926.
  • [Has2] F. Haslinger, Singularities of the Szegő kernel for certain weakly pseudoconvex domains in $ℂ^2$, J. Funct. Anal. 129 (1995), 406-427.
  • [Has3] F. Haslinger, Bergman and Hardy spaces on model domains, Illinois J. Math. (to appear).
  • [He] P. Henrici, Applied and Computational Complex Analysis, II, Wiley, New York, 1977.
  • [K] H. Kang, $∂̅_b$-equations on certain unbounded weakly pseudoconvex domains, Trans. Amer. Math. Soc. 315 (1989), 389-413.
  • [Kr] S. G. Krantz, Function Theory of Several Complex Variables, Wadsworth & Brooks/Cole, Pacific Grove, Calif., 1992.
  • [McN1] J. McNeal, Boundary behavior of the Bergman kernel function in $ℂ^2$, Duke Math. J. 58 (1989), 499-512.
  • [McN2] J. McNeal, Local geometry of decoupled pseudoconvex domains, in: Complex Analysis, Aspects of Math. E17, K. Diederich (ed.), Vieweg 1991, 223-230.
  • [McN3] J. McNeal, Estimates on the Bergman kernels on convex domains, Adv. Math. 109 (1994), 108-139.
  • [N] A. Nagel, Vector fields and nonisotropic metrics, in: Beijing Lectures in Harmonic Analysis, E. M. Stein (ed.), Princeton Univ. Press, Princeton, N.J., 1986, 241-306.
  • [NRSW1] A. Nagel, J. P. Rosay, E. M. Stein and S. Wainger, Estimates for the Bergman and Szegő kernels in certain weakly pseudoconvex domains, Bull. Amer. Math. Soc. 18 (1988), 55-59.
  • [NRSW2] A. Nagel, J. P. Rosay, E. M. Stein and S. Wainger, Estimates for the Bergman and Szegő kernels in $ℂ^2$, Ann. of Math. 129 (1989), 113-149.
  • [OPY] K. Oeljeklaus, P. Pflug and E. H. Youssfi, The Bergman kernel of the minimal ball and applications, Ann. Inst. Fourier (Grenoble) 47 (1997), 915-928.
  • [R] M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, 1986.
  • [S] E. M. Stein, Harmonic Analysis. Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, N.J., 1993.
  • [T] B. A. Taylor, On weighted polynomial approximation of entire functions, Pacific J. Math. 36 (1971), 523-539.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv70z1p109bwm
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