11,536 research outputs found
Spatial discretization of restricted group algebras
We consider spatial discretizations by the finite section method of the
restricted group algebra of a finitely generated discrete group, which is
represented as a concrete operator algebra via its left-regular representation.
Special emphasis is paid to the quasicommutator ideal of the algebra generated
by the finite sections sequences and to the stability of sequences in that
algebra. For both problems, the sequence of the discrete boundaries plays an
essential role. Finally, for commutative groups and for free non-commutative
groups, the algebras of the finite sections sequences are shown to be fractal
An analytical comparison of coalescent-based multilocus methods: The three-taxon case
Incomplete lineage sorting (ILS) is a common source of gene tree incongruence
in multilocus analyses. A large number of methods have been developed to infer
species trees in the presence of ILS. Here we provide a mathematical analysis
of several coalescent-based methods. Our analysis is performed on a three-taxon
species tree and assumes that the gene trees are correctly reconstructed along
with their branch lengths
Semi-classical trace formula, isochronous case. Application to conservative systems
Under conditions of clean flow we compute the leading term in the STF when
the set of periods of the energy surface is discrete. Comparing to the case of
non-degenerate periodic orbits, we obtain a supplementary term which is given
in terms of the linearized flow. As particular cases, we give a STF for
quadratic Hamiltonians and we obtain the Berry-Tabor formula for integrable
systems. For conservative systems (i.e. systems with several first integrals),
we give practical conditions to get a clean flow and interpret the leading term
of the STF for a compact symmetry. We give several examples to illustrate our
computation.Comment: 24 page
Finite sections of truncated Toeplitz operators
We describe the -algebra associated with the finite sections
discretization of truncated Toeplitz operators on the model space where
is an infinite Blaschke product. As consequences, we get a stability
criterion for the finite sections discretization and results on spectral and
pseudospectral approximation.Comment: 12 page
Reduced Gutzwiller formula with symmetry: case of a Lie group
We consider a classical Hamiltonian on , invariant by a
Lie group of symmetry , whose Weyl quantization is a selfadjoint
operator on . If is an irreducible character of ,
we investigate the spectrum of its restriction to the
symmetry subspace of coming
from the decomposition of Peter-Weyl. We give semi-classical Weyl asymptotics
for the eigenvalues counting function of in an interval of
, and interpret it geometrically in terms of dynamics in the
reduced space . Besides, oscillations of the spectral
density of are described by a Gutzwiller trace formula
involving periodic orbits of the reduced space, corresponding to quasi-periodic
orbits of .Comment: 23 page
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