Nonlinear approximation by renormalized trigonometric system

We study the convergence of greedy algorithmwith regard to renormalized trigonometric system. Necessary and sufficient conditions are found for system’s normalization to guarantee almost everywhere convergence, and convergence in L ^p (T) for 1 < p < ∞ of the greedy algorithm, where T is the unit torus. Also the non existence is proved for normalization which guarantees convergence almost everywhere for functions from L ¹(T), or uniform convergence for continuous functions.