Search results for "Invariant"

Biweights on Partial *-Algebras

2000

This chapter is devoted to the systematic investigation of biweights on partial *-algebras. These are a generalization of invariant positive sesquilinear forms that still allows a Gel’fand—Naĭmark—Segal (GNS) construction of representations. In Section 9.1, we apply this GNS construction for biweights and we obtain *-representations and cyclic vector representations of partial *-algebras, and we give some examples of biweights. Section 9.2 is devoted to the investigation of the Radon—Nikodým theorem and the Lebesgue decomposition theorem for biweights on partial *-algebras. In Section 9.3, we define regular and singular biweights on partial *-algebras and we characterize them with help of t…

Dimension of self-affine sets for fixed translation vectors

2018

An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently ver…

Stability conditions and related filtrations for $(G,h)$-constellations

2017

Given an infinite reductive algebraic group $G$, we consider $G$-equivariant coherent sheaves with prescribed multiplicities, called $(G,h)$-constellations, for which two stability notions arise. The first one is analogous to the $\theta$-stability defined for quiver representations by King and for $G$-constellations by Craw and Ishii, but depending on infinitely many parameters. The second one comes from Geometric Invariant Theory in the construction of a moduli space for $(G,h)$-constellations, and depends on some finite subset $D$ of the isomorphy classes of irreducible representations of $G$. We show that these two stability notions do not coincide, answering negatively a question raise…

Bounded elements in certain topological partial *-algebras

2011

We continue our study of topological partial *algebras, focusing our attention to the interplay between the various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between the strong and the weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *algebras, emphasizing the crucial role played by appropriate bounded elements, called $\M$-bounded. Finally, some remarks are made concerning representations in terms of the so-called partial GC*-algebras of operators.

Quantization on the Virasoro group

1990

The quantization of the Virasoro group is carried out by means of a previously established group approach to quantization. We explicitly work out the two-cocycles on the Virasoro group as a preliminary step. In our scheme the carrier space for all the Virasoro representations is made out of polarized functions on the group manifold. It is proved that this space does not contain null vector states, even forc≦1, although it is not irreducible. The full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace ℋ(c, h), the orbit of the enveloping algebra through the vacuum, which is irreducible for any value ofc andh. ℋ(c, h) is a proper subspace of the sp…

Inner functions and local shape of orthonormal wavelets

2011

Abstract Conditions characterizing all orthonormal wavelets of L 2 ( R ) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs, the so-called Haar bases, leads to new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces articulate the structure of these families. The new algorithms focus on the local shape of the wavelet.

An invariant analytic orthonormalization procedure with an application to coherent states

2007

We discuss a general strategy which produces an orthonormal set of vectors, stable under the action of a given set of unitary operators Aj, j=1,2,n, starting from a fixed normalized vector in H and from a set of unitary operators. We discuss several examples of this procedure and, in particular, we show how a set of coherentlike vectors can be produced and in which condition over the lattice spacing this can be done. © 2007 American Institute of Physics.

On the index form of a geodesic in a pseudoriemannian almost-product manifold

1986

Varieties of representations of virtual knot groups in SL2(C)

2002

Abstract We study the local structure of the variety of representations of a virtual knot group in SL 2 ( C ) near an abelian representation ρ 0 . To such a representation is attached a complex number ω and there are three cases. If ω and ω −1 are not roots of the Alexander polynomial, there are only abelian representations around ρ 0 . If ω is a root and ω −1 is not, there are only reducible representations. If both ω and ω −1 are roots and certain homological conditions hold, there are irreducible representations.

Singular levels and topological invariants of Morse Bott integrable systems on surfaces

2016

Abstract We classify up to homeomorphisms closed curves and eights of saddle points on orientable closed surfaces. This classification is applied to Morse Bott foliations and Morse Bott integrable systems allowing us to define a complete invariant. We state also a realization Theorem based in two transformations and one generator (the foliation of the sphere with two centers).