$L^p$-Conjecture on 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

An Lp Version of the Beck-Fiala Conjecture

Beck and Fiala conjectured in 1981 that for any set system S of maximum degree t on a nite ground set X, a coloring : X ! f?1; +1g exists such that j(S)j = O(p t) holds for all S 2 S, where (S) = P x2S (X). We prove a weaker statement, namely that for any xed p 1, a coloring exists such that the pth degree average of j(S)j over S 2 S is O(p t). The result also holds if each set is assigned a no...

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 ...

On α-amenability of commutative hypergroups

We study the concept of α-amenability of commutative hypergroups K. We establish several characterizations of α-amenability by combining results of [1] and [2] and adding the Glicksberg-Reiter property. In addition, as examples compact K and discrete polynomial hypergroups on N0 are discussed. 2000 Mathematics Subject Classification: Primary 43A62, Secondary 46H25