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. The usual convolution of class functions on a connected reductive group over a finite field makes sense also for complexes in D(G0) and then it preserves (see [Gi])...

We present a comparative study of four product operators on weighted languages: (i) the convolution, (ii) the shuffle, (iii) the infiltration, and (iv) the Hadamard product. Exploiting the fact that the set of weighted languages is a final coalgebra, we use coinduction to prove that a classical operator from difference calculus in mathematics: the Newton transform, generalises (from infinite se...

In the early fties L. Schwartz posed the problem to characterize those linear partial differential operators P(D) that admit a (continuous linear) right inverse on the Fr echet space E(() of all innnitely diierentiable functions on an open set in IR n respectively on the space D 0 (() of all distributions on. This problem was solved in 6], 7]. Its solution was extended to diierential complexes ...

Let α : G → G be an endomorphism of a discrete amenable group such that [G : α(G)] < ∞. We study the structure of the C∗ algebra generated by the left convolution operators acting on the left regular representation space, along with the isometry of the space induced by the endomorphism.

Let M(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup S with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for M(S)∗ to have a topologically left invariant mean.

A short review of the use of quantum groups to addition theorems for q-special functions is given. We discuss a general convolution formula for Al-Salam and Chihara polynomials arising from its quantum algebra as transition coeecients. This contribution does not contain new results.

Judicious use of number theory and abstract algebra can increase the eeciency of neural network pattern classiiers. We use the example of our neural network tissue classiication of MRI of the breast to illustrate that eecient pattern recognition algorithms can be designed from algebraic fundamentals. The algorithm is based on number theoretic transform speed-up of an FFT-based convolution scheme.

In this paper we study the computation of a set of bilinear forms associated with a finite group. In the case of a cyclic group these bilinear forms represent the well-knowrl circular convolution of two sequences and can be evaluated efficiently using the fast finite Fourier transform. WC shall use a similar technique in the case of a general finite group and will apply it to calculate gror;p a...

In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters are solutions of some differential equations which are of the same type as the differential equations used to describe the renormalization group flow in qua...

We present an intrinsically defined algebra of operators containing the right and left invariant Calderón-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on Lp (1 < p <∞). This algebra provides an example of an algebra of singular integrals that falls outside of the classical Calderón-Zygmund theory.