"Basis and regularity properties of (p,q)-trigonometric functions and the decay of (p,q)-Fourier coefficients"

The basis and regularity properties of the generalized trigonometric functions sinp,q and cosp,q are investigated. Upper bounds for the Fourier coefficients of these functions are given. Conditions are obtained under which the functions cosp,q generate a basis of every Lebesgue space Lr(0,1) with 12 are calculable numbers. A comparison is made of the speed of decay of the Fourier sine coefficients of a function in Lebesgue and Lorentz sequence spaces with that of the corresponding coefficients with respect to the functions sinp,q.These results sharpen previously known ones.

Keywords: basis; fourier coefficients; trigonometric functions; basis regularity; regularity properties; decay fourier

Journal Title: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Year Published: 2018

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