In this paper we generalize Wiener’s characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and nilmanifolds to be continuous. The methods use only simple properties of heat kernels.
We prove three theorems on linear operators induced by rearrangement of a subsequence of a Haar system. We find a sufficient and necessary condition for to be continuous for 0 < p < ∞.
In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.
On montre que si est une contraction à spectre dénombrable et telle que, pour tout
We show that the dual version of our factorization [J. Funct. Anal. 261 (2011)] of contractive homomorphisms φ: L¹(F) → M(G) between group/measure algebras fails to hold in the dual, Fourier/Fourier-Stieltjes algebra, setting. We characterize the contractive w*-w* continuous homomorphisms between measure algebras and (reduced) Fourier-Stieltjes algebras. We consider the problem of describing all contractive homomorphisms φ: L¹(F) → L¹(G).
We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces , where G is a homogeneous group.
Let be a hypergroup. In this paper, we define a locally convex topology on such that with the strong topology can be identified with a Banach subspace of . We prove that if has a Haar measure, then the dual to this subspace is has compact carrier}. Moreover, we study the operators on and which commute with translations and convolutions. We prove, among other things, that if is left stationary, then there is a weakly compact operator on which commutes with convolutions if and...
Mathematics Subject Classification: 43A20, 26A33 (main), 44A10, 44A15We prove equalities in the Banach algebra L1(R+). We apply them to integral transforms and fractional calculus.* Partially supported by Project BFM2001-1793 of the MCYT-DGI and FEDER and Project E-12/25 of D.G.A.