24 citations · 29 across the 15 of their papers we have counts for
6 papers · 2 filters
Analysis and geometry on worm domains
Steven G. Krantz, Marco M. Peloso
We describe recent work on the Bergman kernel of the (non-smooth) worm domain in several complex variables. An asymptotic expansion is obtained for the Bergman kernel. Mapping prop…
Topologies on the space of holomorphic functions
Steven G. Krantz
We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it tu…
The Bergman kernel and projection on non-smooth worm domains
Steven G. Krantz, Marco M. Peloso
This paper provides a precise asymptotic expansion for the Bergman kernel on the non-smooth worm domains of Christer Kiselman in complex 2-space. Applications are given to the fail…
A new look at convexity and pseudoconvexity
Steven G. Krantz
We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs.
Complex Analysis as Catalyst
Steven G. Krantz
We illustrate the general principle that complex analysis can be a good setting for posing problems that are best solved using techniques from other mathematical disciplines. Sever…
The Caratheodory-Cartan-Kaup-Wu theorem on an infinite dimensional Hilbert space
Joseph Cima, Ian Graham, Kang-Tae Kim +1
This paper treats a holomorphic self-mapping f: Omega --> Omega of a bounded domain Omega in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prov…