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Multipliers on homogeneous Banach spaces with respect to Jacobi polynomials. (English) Zbl 1290.43011

The author of the article under review studies multipliers with respect to Jacobi polynomials, i.e., operators that commute with the Jacobi translations on \([-1,1]\). He establishes four characterizations of multipliers on homogeneous Banach spaces on \([-1,1]\). Then the author studies multipliers on certain homogeneous Banach spaces such as the Wiener algebra, the Beurling spaces, Sobolev spaces.

MSC:

43A62 Harmonic analysis on hypergroups
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
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