What the algebra of convolution does for linear systems, the algebra of mathematical morphology does for shape. Since shape is a prime carrier of information in machine vision, there should be little surprise about the importance of the mathematical morphology. Now adays the operations of mathematical morphology are very much useful in object or defect identification required in industrial visi...

The classical Serre-Swan’s theorem defines a bijective correspondence between vector bundles and finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its convolution algebra tha...

Negative results: 1) A convolution R g(?y)h(y) dy need not be measurable with respect to the {algebra generated by the translates of g. 2) There exist a Borel set A R and two {{nite measures , such that R R 1 A (x + y) dd(x)dd(y) 6 = R R 1 A (x + y) dd(y)dd(x). Positive result: A function of two variables, measurable with respect to a product {algebra A B and partially measurable with respect t...

ABSTRACT. Let (a, 6) be any open subinterval of the reals which contains the origin and let 33 denote the family of all distributions on [a, b) which are regular in some interval (e, 0), where e < 0. Then S is a commutative algebra: Multiplication is defined so that, when restricted to those distributions on (a, b) whose supports are contained in [0, b), it is ordinary convolution. Also, S) can...

In this thesis, we investigate two ways of generalising the preprojective algebra. First, we introduce the multiplicative preprojective algebra, Λ(Q), which is a multiplicative analogue of the deformed preprojective algebra, introduced by Crawley-Boevey and Holland. The special case q = 1 is the undeformed multiplicative preprojective algebra, which is an analogue of the ordinary (undeformed) p...

This report describes a Maple package created for exploring the techniques of Winograd, Nussbaumer, and others for computing “fast” convolution algorithms. After codifying known convolution techniques into a common framework of bilinear algorithms built from parameterized matrices and algebraic operators, Maple’s symbolic and algebraic computation facilities are used to derive and manipulate th...

Let G denote a locally compact abelian topological group (an l.c.a. group) with dual group C\ We will denote by A7(G) the Banach algebra of bounded regular Borel measures on G under convolution multiplication and by L(G) the algebra of bounded measures absolutely continuous with respect to Haar measure on G (for discussions of these Banach algebras cf. [1], [2], and [5]). In this paper we shall...

Let K be a locally compact hypergroup. In this paper, among other results we give sufficient condition for the inclusion LΦ1w (K) * LΦ2w ⊆ to hold. Also, as an application, provide new weighted Orlicz space LΦw convolution Banach algebra.

Let G be a locally compact, totally disconnected, Hausdorff topological group with a neighborhood basis {Ki}i of the identity consisting of compact, open, normal subgroups. Often K ⊂ G will denote a compact, open subgroup of G. We consider representations (ρ, V ) of G, where V is often infinite-dimensional. We say the representation is smooth if V = ∪KV K , i.e., if every v ∈ V is fixed by some...