6,235 research outputs found
Invariant Stein domains in Stein symmetric spaces and a non-linear complex convexity theorem
We prove a complex version of Kostant's non-linear convexity theorem.
Applications to the construction of G-invariant Grauert tubes of non-compact
Riemannian symmetric G/K spaces are given.Comment: 9 page
Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces
In this paper we define a distinguished boundary for the complex crowns
\Xi\subeq G_\C /K_\C of non-compact Riemannian symmetric spaces . The
basic result is that affine symmetric spaces of can appear as a component
of this boundary if and only if they are non-compactly causal symmetric spaces.Comment: 29 page
Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions
Kernel mean embeddings have recently attracted the attention of the machine
learning community. They map measures from some set to functions in a
reproducing kernel Hilbert space (RKHS) with kernel . The RKHS distance of
two mapped measures is a semi-metric over . We study three questions.
(I) For a given kernel, what sets can be embedded? (II) When is the
embedding injective over (in which case is a metric)? (III) How does
the -induced topology compare to other topologies on ? The existing
machine learning literature has addressed these questions in cases where is
(a subset of) the finite regular Borel measures. We unify, improve and
generalise those results. Our approach naturally leads to continuous and
possibly even injective embeddings of (Schwartz-) distributions, i.e.,
generalised measures, but the reader is free to focus on measures only. In
particular, we systemise and extend various (partly known) equivalences between
different notions of universal, characteristic and strictly positive definite
kernels, and show that on an underlying locally compact Hausdorff space,
metrises the weak convergence of probability measures if and only if is
continuous and characteristic.Comment: Old and longer version of the JMLR paper with same title (published
2018). Please start with the JMLR version. 55 pages (33 pages main text, 22
pages appendix), 2 tables, 1 figure (in appendix
Holomorphic horospherical transform on non-compactly causal spaces
We develop integral geometry for non-compactly causal symmetric spaces. We
define a complex horospherical transform and, for some cases, identify it with
a Cauchy type integral.Comment: Revised, final version; to appear in IMRN, 38
AlScN: A III-V semiconductor based ferroelectric
Ferroelectric switching is unambigiously demonstrated for the first time in a
III-V semiconductor based material: AlScN -- A discovery which could help to
satisfy the urgent demand for thin film ferroelectrics with high performance
and good technological compatibility with generic semiconductor technology
which arises from a multitude of memory, micro/nano-actuator and emerging
applications based on controlling electrical polarization. The appearance of
ferroelectricity in AlScN can be related to the continuous distortion of the
original wurtzite-type crystal structure towards a layered-hexagonal structure
with increasing Sc content and tensile strain, which is expected to be
extendable to other III-nitride based solid solutions. Coercive fields which
are systematically adjustable by more than 3 MV/cm, high remnant polarizations
in excess of 100 \mu C/cm which constitute the first experimental estimate
of the previously inaccessible spontaneous polarization in a III-nitride based
material, an almost ideally square-like hysteresis resulting in excellent
piezoelectric linearity over a wide strain interval from -0.3% to +0.4% as well
as a paraelectric transition temperature in excess of 600{\deg}C are confirmed.
This intriguing combination of properties is to our knowledge as of now
unprecedented in the field of polycrystalline ferroelectric thin films and
promises to significantly advance the commencing integration of ferroelectric
functionality to micro- and nanotechnology, while at the same time providing
substantial insight to one of the central open questions of the III-nitride
semiconductors - that of their actual spontaneous polarization
- …