Steven G. Krantz
Canonical kernels versus constructible kernels.
Ср, 12/07/2011 - 15:01 — SomNambulAuthors: Steven G. Krantz
Subjects: Complex Variables
AbstractWe study both canonical reproducing kernels and constructive reproducing
kernels for holomorphic functions in $\CC^1$ and $\CC^n$. We compare and
contrast the two, and also develop important relations between the two types of
kernels. We prove a new result about the relationship between these two kernels
on certain domains of finite type.The Carath\'{e}odory and Kobayashi/Royden Metrics by Way of Dual Extremal Problems.
Ср, 06/01/2011 - 15:01 — SomNambulAuthors: Steven G. Krantz, Halsey Royden, Pit-Mann Wong
Subjects: Complex Variables
AbstractWe study the Carath\'{e}odory and Kobayashi metrics by way of the method of
dual extremal problems in functional analysis. Particularly incisive results
are obtained for convex domains.- 1 комментарий
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The corona problem with two pieces of data.
Ср, 01/13/2010 - 16:01 — SomNambulAuthors: Steven G. Krantz
Subjects: Complex Variables
AbstractWe study the corona problem on the unit ball in $\CC^n$, and more generally
on strongly pseudoconvex domains in $\CC^n$. When the corona problem has just
two pieces of data, and an extra geometric hypothesis is satisfied, then we are
able to solve it.The Schwarz lemma at the boundary.
Ср, 01/13/2010 - 16:01 — SomNambulAuthors: Steven G. Krantz
Subjects: Complex Variables
AbstractThe most classical version of the Schwarz lemma involves the behavior at the
origin of a bounded, holomorphic function on the disc. Pick's version of the
Schwarz lemma allows one to move the origin to other points of the disc.In the present paper we explore versions of the Schwarz lemma at a boundary
point of a domain (not just the disc). Estimates on derivatives of the
function, and other types of estimates as well, are considered. We review
recent results of several authors, and present some new theorems as well.The Kobayashi metric, extremal discs, and biholomorphic mappings.
Втр, 09/08/2009 - 12:16 — SomNambulAuthors: Steven G. Krantz
Subjects: Complex Variables
AbstractWe study extremal discs for the Kobayashi metric. Inspired by work of Lempert
on strongly convex domains, we present results on strongly pseudoconvex
domains.We also consider a useful biholomorphic invariant, inspired by the Kobayashi
(and Carath\'{e}odory) metric, and prove several new results about
biholomorphic equivalence of domains. Some useful results about automorphism
groups of complex domains are also established.Normed domains of holomorphy.
Втр, 09/01/2009 - 12:47 — SomNambulAuthors: Steven G. Krantz
Subjects: Complex Variables
AbstractWe treat the classical concept of domain of holomorphy in $\CC^n$ when the
holomorphic functions considered are restricted to lie in some Banach space.
Positive and negative results are presented. A new view of the case $n = 1$ is
considered.- 2 комментария
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Normed domains of holomorphy.
Втр, 09/01/2009 - 12:47 — SomNambulAuthors: Steven G. Krantz
Subjects: Complex Variables
AbstractWe treat the classical concept of domain of holomorphy in $\CC^n$ when the
holomorphic functions considered are restricted to lie in some Banach space.
Positive and negative results are presented. A new view of the case $n = 1$ is
considered.Convexity in real analysis.
Втр, 09/01/2009 - 12:47 — SomNambulAuthors: Steven G. Krantz
Subjects: Classical Analysis and ODEs
AbstractWe treat the classical notion of convexity in the context of hard real
analysis. Definitions of the concept are given in terms of defining functions
and quadratic forms, and characterizations are provided of different concrete
notions of convexity. This analytic notion of convexity is related to more
classical geometric ideas. Applications are given both to analysis and
geometry.
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