We show that an unbounded measure on a strong commutative hypergroup is transformable if and only if its convolution with any positive definite function of compact support is positive definite.
Proviamo che una misura illimitata su un ipergruppo fortemente commutativo è trasformabile se e solo se la sua convoluzione con una qualunque funzione definita positiva a supporto compatto è definita positiva.
@article{BUMI_2007_8_10B_3_819_0, author = {Massoud Amini}, title = {Fourier Transform of Unbounded Measures on Hypergroups}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {10-A}, year = {2007}, pages = {819-828}, zbl = {1185.43003}, mrnumber = {2507898}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_819_0} }
Amini, Massoud. Fourier Transform of Unbounded Measures on Hypergroups. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 819-828. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_819_0/
[AL] 145, American Mathematical Society, Providence, R.I., 1974. | MR 621876 | Zbl 0294.43002
- , Fourier analysis of unbounded measures on locally compact abelian groups, Memoirs of the American Mathematical Society, No.[AM] Fourier algebras on tensor hypergrups, Contemporary Math. 363 (2004), 1-14. | MR 2097946 | Zbl 1061.43010
- ,[B] Diffraction of weighted lattice subsets, Canad. Math. Bull.45, no. 4 (2002), 483-498. | MR 1941223 | Zbl 1161.52309
,[BH] 20, Walter de Gruyter, Berlin, New York, 1995. | MR 1312826 | Zbl 0828.43005
, , Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Mathematics[Bo] | MR 209424
, Elements de Mathematique, Integration, 2nd ed., Herman, Paris, 1965.[E] algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France92 (1964), 181-236. | MR 228628 | Zbl 0169.46403
, L'[GM] Compact multipliers on weighted hypergroup algebras I, II, Math. Proc. Camb. Phil. Soc. 98 (1985), 493-500, 100 (1986), 145-149. | MR 838661 | Zbl 0584.43004
- ,[Je] Spaces with an abstract convolution of measures, Advances in Math.18 (1975), 1-110. | MR 394034
, , Fourier analysis on groups, Wiley Classics Library, John Wiley and Sons, Inc., New York, 1990.