Search results for " representation"
showing 10 items of 811 documents
Representation and estimation of spectral reflectances using projection on PCA and wavelet bases
2008
In this article, we deal with the problem of spectral reflectance function representation and estimation in the context of multispectral imaging. Because the reconstruction of such functions is an inverse problem, slight variations in input data completely skew the expected results. Therefore, stabilizing the reconstruction process is necessary. To do this, we propose to use wavelets as basis functions, and we compare those with Fourier and PCA bases. We present the idea and compare these three methods, which belong to the class of linear models. The PCA method is training-set dependent and confirms its robustness when applied to reflectance estimation of the training sets. Fourier and wave…
On Radon transforms on compact Lie groups
2016
We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to $S^1$ nor to $S^3$. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms from $S^1$.
On the stability of flat complex vector bundles over parallelizable manifolds
2017
We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / \Gamma$, where $G$ is a complex connected Lie group and $\Gamma$ is a cocompact lattice in it. The main result proved here is a structure theorem for flat holomorphic vector bundles $E_\rho$ associated to any irreducible representation $\rho : \Gamma \rightarrow \text{GL}(r,{\mathbb C})$. More precisely, we prove that $E_{\rho}$ is holomorphically isomorphic to a vector bundle of the form $E^{\oplus n}$, where $E$ is a stable vector bundle. All the rational Chern classes of $E$ vanish, in particular, its degree is zero. We deduce a stability result for flat holomorphic vector bundles $E_{\r…
The Bianchi variety
2010
The totality Lie(V) of all Lie algebra structures on a vector space V over a field F is an algebraic variety over F on which the group GL(V) acts naturally. We give an explicit description of Lie(V) for dim V=3 which is based on the notion of compatibility of Lie algebra structures.
Symplectic Applicability of Lagrangian Surfaces
2009
We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equa- tions. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.
A Classification of Modular Functors via Factorization Homology
2022
Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be described as modular algebras over central extensions of the modular surface operad, with the values of the algebra lying in a suitable symmetric monoidal $(2,1)$-category $\mathcal{S}$ of linear categories. In this paper, we prove that modular functors in $\mathcal{S}$ are equivalent to self-dual balanced braided algebras $\mathcal{A}$ in $\mathcal{S}$ (a categorification of the notion of a commutative Frobenius algebra) for which a condition formulated in terms of factorization homology with coefficients in $\mathcal{…
The distinguished invertible object as ribbon dualizing object in the Drinfeld center
2022
We prove that the Drinfeld center $Z(\mathcal{C})$ of a pivotal finite tensor category $\mathcal{C}$ comes with the structure of a ribbon Grothendieck-Verdier category in the sense of Boyarchenko-Drinfeld. Phrased operadically, this makes $Z(\mathcal{C})$ into a cyclic algebra over the framed $E_2$-operad. The underlying object of the dualizing object is the distinguished invertible object of $\mathcal{C}$ appearing in the well-known Radford isomorphism of Etingof-Nikshych-Ostrik. Up to equivalence, this is the unique ribbon Grothendieck-Verdier structure on $Z(\mathcal{C})$ extending the canonical balanced braided structure that $Z(\mathcal{C})$ already comes equipped with. The duality fun…
Transport equations and quasi-invariant flows on the Wiener space
2010
Abstract We shall investigate on vector fields of low regularity on the Wiener space, with divergence having low exponential integrability. We prove that the vector field generates a flow of quasi-invariant measurable maps with density belonging to the space L log L . An explicit expression for the density is also given.
Complex group algebras of finite groups: Brauer's Problem 1
2007
Abstract Brauer's Problem 1 asks the following: What are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to present a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m of isomorphic summands, then its dimension is bounded in terms of m . We prove that this is true for every finite group if it is true for the symmetric groups. The problem for symmetric groups reduces to an explicitly stated question in number theory or combinatorics.
Equivalence Relations on Stonian Spaces
1996
Abstract Quotient spaces of locally compact Stonian spaces which generalize in some sense the concept of Stone representation space of a Boolean algebra are investigated emphasizing the measure theoretical point of view, and a representation theorem for finitely additive measures is proved.