On dihedral hypergroups

on semihypergroups and hypergroups

in this thesis, first the notion of weak mutual associativity (w.m.a.) and the necessary and sufficient condition for a $(l,gamma)$-associated hypersemigroup $(h, ast)$ derived from some family of $lesssim$-preordered semigroups to be a hypergroup, are given. second, by proving the fact that the concrete categories, semihypergroups and hypergroups have not free objects we will introduce t...

On weak Γ-(semi)hypergroups

$L^p$-Conjecture on Hypergroups

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

Spectral Synthesis in Segal Algebras on Hypergroups

Warner (1966), Hewitt and Ross (1970), Yap (1970), and Yap (1971) extended the so-called Ditkin's condition for the group algebra L\G) of a locally compact abelian group G to the algebras L(G) Π L(G), dense subalgebras of L{G) which are essential Banach LHO-modules, LKG) Π L(G)(1 ^ p < co) and Segal algebras respectively. Chilana and Ross (1978) proved that the algebra L^K) satisfies a stronger...

Deformations of Convolution Semigroups on Commutative Hypergroups

It was recently shown by the authors that deformations of hypergroup convolutions w.r.t. positive semicharacters can be used to explain probabilistic connections between the Gelfand pairs (SL(d, C), SU(d)) and Hermitian matrices. We here study connections between general convolution semigroups on commutative hypergroups and their deformations. We are able to develop a satisfying theory, if the ...