Modern techniques treat color images as separate monochrome images for processing. Partly, because there is no straightforward generalization of linear filters available for color. However the algorithms yield more accurate results when the correlation among color bands are exploited which shows fundamental difference to process the color images. Earlier work[8] reported the transformation of t...

ABSTRACT. The key result in the paper concerns two transformations, Φ : (ρ, ψ) 7→ φ and Bt : ψ 7→ φ, where ρ, ψ, φ are states on the algebra of non-commutative polynomials, or equivalently joint distributions of d-tuples of non-commuting operators. These transformations are related to free probability: if ⊞ is the free convolution operation, and {ρt} is a free convolution semigroup, we show tha...

The purpose of this paper is to prove two theorems which concern the position of étale groupoids among general smooth (or ”Lie”) groupoids. Our motivation comes from the non-commutative geometry and algebraic topology concerning leaf spaces of foliations. Here, one is concerned with invariants of the holonomy groupoid of a foliation [4, 34], such as the cohomology of its classifying space [14],...

Bessel-type convolution algebras of bounded Borel measures on the matrix cones of positive semidefinite q×q-matrices over R,C,H were introduced recently by Rösler. These convolutions depend on some continuous parameter, generate commutative hypergroup structures and have Bessel functions of matrix argument as characters. Here, we first study the rich algebraic structure of these hypergroups. In...

Throughout this paper, G denotes a fixed, not necessarily connected, reductive algebraic group over an algebraically closed field k. This paper is a part of a series [L9] which attempts to develop a theory of character sheaves on G. One of the main constructions in [L3] (going back to [L14]) was a procedure which to any character sheaf on G associates a certain two-sided cell in an (extended) C...

For an increasing sequence (ωn) of algebra weights on R + we study various properties of the Fréchet algebra A(ω) = ⋂ n L (ωn) obtained as the intersection of the weighted Banach algebras L(ωn). We show that every endomorphism of A(ω) is standard, if for all n ∈ N there exists m ∈ N such that ωm(t)/ωn(t) → ∞ as t → ∞. Moreover, we characterise the continuous derivations on this algebra: If for ...

Intracellular recordings in spinal cord motoneurons and cerebral cortex neurons have provided new evidence on the correlational strength of monosynaptic connections, and the relation between the shapes of postsynaptic potentials and the associated increased firing probability. In these cells, excitatory postsynaptic potentials (EPSPs) produce crosscorrelogram peaks which resemble in large part ...

We present a method for obtaining asymptotics for the generic element of a two-dimensional convolution matrix which includes Stirling numbers of both kinds and some other interesting combinatorial quantities. Asy2dim is a computer algebra package which implement this method. The current version of Asy2dim is written in Maple V.3 2]. R esum e Nous pr esentons une m ethode pour calculer l' evalua...

To study operator algebras with symmetries in a wide sense we introduce a notion of relative convolution operators induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already studied (operators of multiplication, usual group convolutions, two-sided convolution etc.) and their different combinations. Basic properties of relative convolutio...

Modern data processing applications execute increasingly sophisticated analysis that requires operations beyond traditional relational algebra. As a result, operators in query plans grow in diversity and complexity. Designing query optimizer rules and cost models to choose physical operators for all of these novel logical operators is impractical. To address this challenge, we develop Cuttlefis...