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On the Bézout equation in the ring of periodic distributions

Rudolf Rupp, Amol Sasane (2016)

Topological Algebra and its Applications

A corona type theorem is given for the ring D'A(Rd) of periodic distributions in Rd in terms of the sequence of Fourier coefficients of these distributions,which have at most polynomial growth. It is also shown that the Bass stable rank and the topological stable rank of D'A(Rd) are both equal to 1.

On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

Krasniqi, Xhevat Z. (2013)

Mathematica Balkanica New Series

MSC 2010: 42A32; 42A20In this paper we have defined a new class of double numerical sequences. If the coefficients of a double cosine or sine trigonometric series belong to the such classes, then it is verified that they are Fourier series or equivalently their sums are integrable functions. In addition, we obtain an estimate for the mixed modulus of smoothness of a double sine Fourier series whose coefficients belong to the new class of sequences mention above.

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