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We demonstrate that the Fourier partial sums of a Lipschitz continuous function on the two-dimensional special unitary group converge uniformly to the function. [ABSTRACT FROM AUTHOR]

An approximation of functions in Müntz spaces M Λ , L 1 of L 1 functions is studied with the help of Fourier series. Müntz spaces are considered with the Müntz condition and the gap condition imposed. It is proved that up to an isomorphism such spaces are contained in Weil–Nagy's class. Moreover, existence of Schauder bases in Müntz spaces M Λ , L 1 is investigated. [ABSTRACT FROM AUTHOR]

For given p ∈ [ 1 , ∞ ] and g ∈ L p ( R ) , we establish the existence and uniqueness of solutions f ∈ L p ( R ) , to the equation f ( x ) − a f ( b x ) = g ( x ) , where a ∈ R , b ∈ R ∖ { 0 } , and | a | ≠ | b | 1 / p . Solutions include well-known nowhere differentiable functions such as those of Bolzano, Weierstrass, Hardy, and many others. Connections and consequences in the theory of fractal interpolation, approximation theory, and Fourier analysis are established. [ABSTRACT FROM AUTHOR]

This paper deals with the de la Vallée Poussin means of the triangular partial sums of multivariate Fourier series. We determine the exact order of the corresponding operator norms. The lower estimation of these norms will be extended to a class of projection operators having similar projection properties as the de la Vallée Poussin mean. [ABSTRACT FROM AUTHOR]