We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following Malvenuto and Reutenauer, we pass from symmetric functions to non-commutative symmetric functions and from there to the algebra of permutations in order to relate...

We describe a hierarchical technique that allows a class of non-deterministic timed Petri nets to be analyzed using the (max,+) algebra of periodic signals. We show that the timing and controllability analysis of such systems is possible via the use of (supand) inf-convolution operations within the (max,+) framework. We apply this technique to the verification of timing constraints in an intell...

Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebra Ŝ of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or co...

In this note, we give an effective description of the tensor product k[[X]] ⊗k k[[Y ]]. This latter ring is well known to be not isomorphic to k[[X,Y ]]. The effective description we provide is given through the identification of k[[X,Y ]] with a convolution algebra. As an application, we prove that the group structure of Ak does not descend to Spec k[[X]]. Mathematics Subject Classification: 1...

1. Let G be a locally compact and abelian group, Gl the dual group. Through this paper, "Ml will denote the set of all bounded Radon measure n on G; this set will be considered as a Banach algebra when provided with the customary norm as the dual of the space Co(G) defined below and with the ring product defined as convolution. If /iGM1, its Fourier transform is by definition the bounded and co...

We consider in this paper gauge transformations on locally trivial quantum principal fibre bundles (QPFB). If P , B, H , are the algebras of the total space, the base space, the structure group of the bundle, left (right) gauge transformations are defined as automorphisms of the left (right) B-module P which are adapted to the coaction of the Hopf algebra H and to the covering related to the lo...

We consider the problem of identifying the maximal ideals of a Banach algebra S that is contained in a larger Banach algebra B. If S is dense in B in an appropriate sense and if the spectral radii in S and B are the same, then S and B have the same maximal ideals. The result is illustrated by two examples of Banach algebras S in which the density and spectral radius conditions are easily shown ...

the weighted semigroup algebra mb (s, w) is studied via its identification with mb (s) together with a weighted algebra product *w so that (mb (s, w), *) is isometrically isomorphic to (mb (s), *w). this identification enables us to study the relation between regularity and amenability of mb (s, w) and mb (s), and improve some old results from discrete to general case.

Applications of fractional time derivatives in physics and engineering require the existence of nontranslational time automorphisms on the appropriate algebra of observables. The existence of time automorphisms on commutative and noncommutative C∗-algebras for interacting many-body systems is investigated in this article. A mathematical framework is given to discuss local stationarity in time a...