A,(T) = [L9(T) ® LQ(T)]IK where K is the kernel of the convolution operator c:Lp(S>LQ(T)->C0(T) by (f®g)(y)(f* g)(y)-4*(r) is the /?-Fourier algebra which was introduced by Figa-Talamanca in [6] where it was shown that ^ ( T ) * isisometrically isomorphic to MP(T), the bounded, translation invariant, linear operators on LP(T), Herz [11] showed that AP(V) is a Banach algebra under pointwise mult...

A class of desingularizations for orbit closures of representations of Dynkin quivers is constructed, which can be viewed as a graded analogue of the Springer resolution. A stratification of the singular fibres is introduced; its geometry and combinatorics are studied. Via the Hall algebra approach, these constructions relate to bases of quantized enveloping algebras. Using Ginzburg’s theory of...

Recently, interest in shuffle algebra has been renewed due to their connections with multiple zeta values. In this paper, we prove a new shuffle convolution that implies a reduction formula for the multiple zeta value ζ ({5, 1}n).

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C∗-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C∗-subalgebra of M(G)∗ = C0(G) ∗∗. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly com...

and the norm of an element is defined by ||/|| = ƒ | f(t) \ dt. In [4] Rudin showed that every function in L(R) is the convolution of two other functions. In other words, every element of the convolution algebra L(R) can be factored in L 1 ^ )» although this algebra lacks a unit. Subsequently, Cohen [ l ] observed that the essential ingredient in Rudin's argument is that ^(R) has an approximate...

Let G be a reductive, connected algebraic group over an algebraic closure of a finite field. We define a tensor structure on the category of perverse sheaves on G which are direct sums of unipotent character sheaves in a fixed two-sided cell; we show that this is equivalent to the centre with a known monoidal abelian category (a categorification of the J-ring associated to the same two-sided ce...

Braman [1] described a construction where third-order tensors are exactly the set of linear transformations acting on the set of matrices with vectors as scalars. This extends the familiar notion that matrices form the set of all linear transformations over vectors with real-valued scalars. This result is based upon a circulant-based tensor multiplication due to Kilmer et al. [4]. In this work,...

In this paper we present a choreography that explains the process of supervised machine learning. We present how a perceptron (in its dual form) uses convolution kernels to learn to differentiate between two categories of objects. Convolution kernels such as string kernels and tree kernels are widely used in Natural Language Processing (NLP) applications. However, the baggage associated with le...