For a locally compact hypergroup K and a Young function ϕ, we study the Orlicz space L ϕ (K) and provide a sufficient condition for L ϕ (K) to be an algebra under convolution of functions. We show that a closed subspace of L ϕ (K) is a left ideal if and only if it is left translation invariant. We apply the basic theory developed here to characterize the space of multipliers of the Morse-Transue space M ϕ (K). We also investigate the multipliers of L ϕ (S, πK ), where S is the support of the Plancherel measure πK associated to a commutative hypergroup K.
We study the algebraic properties of Generalized Laguerre polynomials for negative integral values of a given parameter which is LFor different values of parameter r, this family provides polynomials which are of great interest. Hajir conjectured that for integers r ≥ 0 and n ≥ 1, L (−1−n−r) n (x) is an irreducible polynomial whose Galois group contains A n , the alternating group on n symbols. Extending earlier results of Schur, Hajir, Sell, Nair and Shorey, we confirm this conjecture for all r ≤ 60. We also prove that L (−1−n−r) n (x) is an irreducible polynomial whose Galois group contains A n whenever n > e r(1+ 1.2762 logr ) .
We prove the classical Hausdor-Young inequality for the Lebesgue spaces on a compact hypergroup using interpolation of sublinear operators. We use this result to prove the Hausdor-Young inequality for Orlicz spaces on a compact hypergroup.
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