Article history: Received 15 May 2009 Accepted 15 August 2009 Available online 2 September 2009 Communicated by Ginette Saracco

A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined Fourier–Bessel series transforms, respectively. Their equivalent relation shown, which the upper bound estimate for best RKHS provided. The convergence rate bounded modulus smoothness, shows that can attain sa...

We consider certain specific exponential sums related to holomorphic cusp forms, give a reformulation for the Lehmer conjecture and prove that certain exponential sums of Fourier coefficients of holomorphic cusp forms contain information on other similar non-overlapping exponential sums. Also, we prove an Omega result for short sums of Fourier coefficients.

The problem of locating the discontinuities of a function by means of its truncated Fourier series, an interesting question in and of itself, arises naturally from an attempt to overcome the Gibbs phenomenon: the poor approximative properties of the Fourier partial sums of a discontinuous function. In [3], Cai et al. developed the idea already introduced in their previous papers and suggested a...