Geodesic
Absolute convergence of expansions in eigen- and adjoint functions of
Izvestiya. Mathematics, Tome 69 (2005) no. 4, pp. 703-717 Cet article a éte moissonné depuis la source Math-Net.Ru

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We establish an analogue of Zygmund's criterion for the absolute convergence of trigonometric Fourier series for expansions in eigen- and adjoint functions of the integral operator $Af(x)=\int_0^{1-x}A(1-x,t)f(t)\,dt$. 
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V. V. Kornev; A. P. Khromov. Absolute convergence of expansions in eigen- and adjoint functions of. Izvestiya. Mathematics, Tome 69 (2005) no. 4, pp. 703-717. http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a2/

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