Spherical functions are Fourier transforms of L 1 -functions
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 6 (1973) no. 4, p. 457-458 
@article{ASENS_1973_4_6_4_457_0,
     author = {Flensted-Jensen, Mogens and Ragozin, David L.},
     title = {Spherical functions are Fourier transforms of $L\_1$-functions},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 6},
     number = {4},
     year = {1973},
     pages = {457-458},
     doi = {10.24033/asens.1255},
     zbl = {0293.22020},
     mrnumber = {51 \#807},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1973_4_6_4_457_0}
}

Flensted-Jensen, Mogens; Ragozin, David L. Spherical functions are Fourier transforms of $L_1$-functions. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 6 (1973) no. 4, pp. 457-458. doi : 10.24033/asens.1255. http://www.numdam.org/item/ASENS_1973_4_6_4_457_0/

[1] T. H. Koornwinder, A short proof of a Paley-Wiener type theorem for the Jacobi transform (Preprint).

[2] B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition (Ann. scient. Éc. Norm. Sup., t. 6, 1973, p. 413-455). | Numdam | MR 51 #806 | Zbl 0293.22019

[3] D. L. Ragozin, Zonal measure algebras on isotropy irreducible homogeneous spaces (Preprint).