Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces

Bronshtein, 1980, The Cauchy problem for hyperbolic operators with characteristics of variable multiplicity, Tr. Mosk. Mat. Obŝ., 41, 83 Bronshtein, 1982, Trans. Mosc. Math. Soc., 1, 87 Bruhat, 1968 Cerezo, 1969, Solution élémentaire d'un opérateur différentiel linéaire invariant à gauche sur un groupe de Lie réel compact et sur un espace homogène réductif compact, Ann. Sci. Éc. Norm. Super., 2, 561, 10.24033/asens.1184 Dickinson, 2002, Perturbations of vector fields on tori: resonant normal forms and Diophantine phenomena, Proc. Edinb. Math. Soc., 45, 731, 10.1017/S001309150000064X Garetto, 2012, On the well-posedness of weakly hyperbolic equations with time dependent coefficients, J. Differ. Equ., 253, 1317, 10.1016/j.jde.2012.05.001 Faraut, 2008 Gröchenig, 2004, Spaces of test functions via the STFT, J. Funct. Spaces Appl., 2, 25, 10.1155/2004/498627 Komatsu, 1973, Ultradistributions, I, J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math., 20, 25 Komatsu, 1977, Ultradistributions, II, J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math., 24, 607 Komatsu, 1982, Ultradistributions, III, J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math., 29, 653 Köthe, 1969 Nishitani, 1983, Sur les équations hyperboliques à coefficients höldériens en t et de classe de Gevrey en x, Bull. Sci. Math., 107, 113 E. Nursultanov, M. Ruzhansky, S. Tikhonov, Nikolskii inequality and Besov, Triebel–Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds, preprint. Ruckle, 1981 Ruzhansky, 2010 Ruzhansky, 2013, Global quantization of pseudo-differential operators on compact Lie groups, SU(2) and 3-sphere, Int. Math. Res. Not., 11, 2439, 10.1093/imrn/rns122 Seeley, 1969, Eigenfunction expansions of analytic functions, Proc. Am. Math. Soc., 21, 734, 10.1090/S0002-9939-1969-0240835-4 Stein, 1970, 10.1515/9781400881871 Taguchi, 1987, Fourier coefficients of periodic functions of Gevrey classes and ultradistributions, Yokohama Math. J., 35, 51 Toft, 2012, The Bargmann transform on modulation and Gelfand–Shilov spaces, with applications to Toeplitz and pseudo-differential operators, J. Pseudo-Differ. Oper. Appl., 3, 145, 10.1007/s11868-011-0044-3 Vilenkin, 1991 Wallach, 1973