133,799 research outputs found
The symmetric Radon-Nikod\'ym property for tensor norms
We introduce the symmetric-Radon-Nikod\'ym property (sRN property) for
finitely generated s-tensor norms of order and prove a Lewis type
theorem for s-tensor norms with this property. As a consequence, if is
a projective s-tensor norm with the sRN property, then for every Asplund space
, the canonical map is a metric surjection. This
can be rephrased as the isometric isomorphism for certain polynomial ideal \Q. We also relate the sRN
property of an s-tensor norm with the Asplund or Radon-Nikod\'{y}m properties
of different tensor products. Similar results for full tensor products are also
given. As an application, results concerning the ideal of -homogeneous
extendible polynomials are obtained, as well as a new proof of the well known
isometric isomorphism between nuclear and integral polynomials on Asplund
spaces.Comment: 17 page
On the Kashiwara-Vergne conjecture
Let be a connected Lie group, with Lie algebra . In 1977, Duflo
constructed a homomorphism of -modules , which restricts
to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a
conjecture on the Campbell-Hausdorff series, which (among other things) extends
the Duflo theorem to germs of bi-invariant distributions on the Lie group .
The main results of the present paper are as follows. (1) Using a recent
result of Torossian (2002), we establish the Kashiwara-Vergne conjecture for
any Lie group . (2) We give a reformulation of the Kashiwara-Vergne property
in terms of Lie algebra cohomology. As a direct corollary, one obtains the
algebra isomorphism , as well as a more general
statement for distributions.Comment: 18 pages, final version, to be published in Inventiones Mat
The Theory of the Interleaving Distance on Multidimensional Persistence Modules
In 2009, Chazal et al. introduced -interleavings of persistence
modules. -interleavings induce a pseudometric on (isomorphism
classes of) persistence modules, the interleaving distance. The definitions of
-interleavings and generalize readily to multidimensional
persistence modules. In this paper, we develop the theory of multidimensional
interleavings, with a view towards applications to topological data analysis.
We present four main results. First, we show that on 1-D persistence modules,
is equal to the bottleneck distance . This result, which first
appeared in an earlier preprint of this paper, has since appeared in several
other places, and is now known as the isometry theorem. Second, we present a
characterization of the -interleaving relation on multidimensional
persistence modules. This expresses transparently the sense in which two
-interleaved modules are algebraically similar. Third, using this
characterization, we show that when we define our persistence modules over a
prime field, satisfies a universality property. This universality result
is the central result of the paper. It says that satisfies a stability
property generalizing one which is known to satisfy, and that in
addition, if is any other pseudometric on multidimensional persistence
modules satisfying the same stability property, then . We also show
that a variant of this universality result holds for , over arbitrary
fields. Finally, we show that restricts to a metric on isomorphism
classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in
Foundations of Computational Mathematics. 36 page
Structural Identifiability Applied to a Heat Transfer System
Identifiability is an essential property of a dynamical model whose study should be addressed before performing any parameter estimation procedure. In this work, we study the structural identifiability of a heat transfer system by making use of the local state isomorphism theorem for two scenarios based on the available experimental measurements.Identifiability is an essential property of a dynamical model whose study should be addressed before performing any parameter estimation procedure. In this work, we study the structural identifiability of a heat transfer system by making use of the local state isomorphism theorem for two scenarios based on the available experimental measurements
Ergodic universality of some topological dynamical systems
The Krieger generator theorem says that every invertible ergodic measure-preserving system with finite measure-theoretic entropy can be embedded into a full shift with strictly greater topological entropy. We extend Krieger's theorem to include toral automorphisms and, more generally, any topological dynamical system on a compact metric space that satisfies almost weak specification, asymptotic entropy expansiveness, and the small boundary property. As a corollary, one obtains a complete solution to a natural generalization of an open problem in Halmos's 1956 book regarding an isomorphism invariant that he proposed
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