22,113 research outputs found
Plancherel formula for Berezin deformation of on Riemannian symmetric space
Consider the space B of complex matrces with norm <1. There
exists a standard one-parameter family of unitary representations of the
pseudounitary group U(p,q) in the space of holomorphic functions on B (i.e.
scalar highest weight representations). Consider the restriction of
to the pseudoorthogonal group O(p,q).
The representation of O(p,q) in on the symmetric space
is a limit of the representations in some
precise sence. Spectrum of a representation is comlicated and it depends
on .
We obtain the complete Plancherel formula for the representations for
all admissible values of the parameter . We also extend this result to
all classical noncompact and compact Riemannian symmetric spaces
Topological properties of concept spaces (full version)
AbstractBased on the observation that the category of concept spaces with the positive information topology is equivalent to the category of countably based T0 topological spaces, we investigate further connections between the learning in the limit model of inductive inference and topology. In particular, we show that the “texts” or “positive presentations” of concepts in inductive inference can be viewed as special cases of the “admissible representations” of computable analysis. We also show that several structural properties of concept spaces have well known topological equivalents. In addition to topological methods, we use algebraic closure operators to analyze the structure of concept spaces, and we show the connection between these two approaches. The goal of this paper is not only to introduce new perspectives to learning theorists, but also to present the field of inductive inference in a way more accessible to domain theorists and topologists
Domain Representable Spaces Defined by Strictly Positive Induction
Recursive domain equations have natural solutions. In particular there are
domains defined by strictly positive induction. The class of countably based
domains gives a computability theory for possibly non-countably based
topological spaces. A space is a topological space characterized by
its strong representability over domains. In this paper, we study strictly
positive inductive definitions for spaces by means of domain
representations, i.e. we show that there exists a canonical fixed point of
every strictly positive operation on spaces.Comment: 48 pages. Accepted for publication in Logical Methods in Computer
Scienc
Domain Representations Induced by Dyadic Subbases
We study domain representations induced by dyadic subbases and show that a
proper dyadic subbase S of a second-countable regular space X induces an
embedding of X in the set of minimal limit elements of a subdomain D of
. In particular, if X is compact, then X is a retract of
the set of limit elements of D
Spectral theory for non-unitary twists
Let be a Lie-group and \Ga\subset G a cocompact lattice. For a
finite-dimensional, not necessarily unitary representation \om of \Ga we
show that the -representation on L^2(\Ga\bs G,\om) admits a complete
filtration with irreducible quotients. As a consequence, we show the trace
formula for non-unitary twists and arbitrary locally compact groups
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