Harmonic analysis and spectral synthesis in central hypergroups
Copyright policy )Harmonic analysis and spectral synthesis in central hypergroups
A locally compact hypergroup K is called central if K/Z is compact where Z is the intersection of the maximal subgroup and the center of K. The dual space of K is shown to be a locally compact Hausdorff space. A Plancherel measure is defined that leads to a simple formulation of the Plancherel theorem and the inversion formula. \(L^ 1(K)\) is shown to be completely regular. It is shown that finite subsets of the dual space are spectral and that their \(L^ 1\)-kernels contain bounded approximate units.
- DigiZeitschriften Germany
- University of Paderborn Germany
spectral synthesis, central hypergroups, dual space, Plancherel theorem, Plancherel measure, approximate units, locally compact hypergroup, Article, 510.mathematics, Spectral synthesis on groups, semigroups, etc., inversion formula, \(L^ 1\)-kernels, Probability measures on groups or semigroups, Fourier transforms, factorization
spectral synthesis, central hypergroups, dual space, Plancherel theorem, Plancherel measure, approximate units, locally compact hypergroup, Article, 510.mathematics, Spectral synthesis on groups, semigroups, etc., inversion formula, \(L^ 1\)-kernels, Probability measures on groups or semigroups, Fourier transforms, factorization
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