On the invariant differential metrics near pseudoconvex boundary points where the Levi form has corank one
Copyright policy )On the invariant differential metrics near pseudoconvex boundary points where the Levi form has corank one
Let D be a bounded domain in Cn; in the space L2(D) of functions on D which are square-integrable with respect to the Lebesgue measure d2nz the holomorphic functions form a closed subspace H2(D). Therefore there exists a well-defined orthogonal projection PD: L2(D) → H2(D) with an integral kernel KD:D × D → C, the Bergman kernel function of D. An explicit computation of this function directly from the definition is possible only in very few cases, as for instance the unit ball, the complex “ellipsoids” , or the annulus in the plane. Also, there is no hope of getting information about the function KD in the interior of a general domain. Therefore the question for an asymptotic formula for the Bergman kernel near the boundary of D arises.
- University of Wuppertal Germany
32H15, bumping lemma, Integral representations; canonical kernels (Szegő, Bergman, etc.), Pseudoconvex domains, plurisubharmonic functions, Cauchy-Riemann equations, 32H10, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Invariant metrics and pseudodistances in several complex variables
32H15, bumping lemma, Integral representations; canonical kernels (Szegő, Bergman, etc.), Pseudoconvex domains, plurisubharmonic functions, Cauchy-Riemann equations, 32H10, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Invariant metrics and pseudodistances in several complex variables
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).9 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!