Abstract:
The author finds a sharp lower bound for the maximal measure of sets on which a Fourier series expansion in a uniformly bounded complete orthonormal system diverges.
This publication is cited in the following 7 articles:
A. Yu. Trynin, “Ob odnom metode resheniya smeshannoi kraevoi zadachi dlya uravneniya parabolicheskogo tipa s pomoschyu operatorov $\mathbb{AT}_{\lambda,j}$”, Izv. vuzov. Matem., 2024, no. 2, 59–80
A. Yu. Trynin, “On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators $\mathbb{A}{{\mathbb{T}}_{{\lambda ,j}}}$”, Russ Math., 68:2 (2024), 52
A. Yu. Trynin, “A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$”, Izv. Math., 87:6 (2023), 1227–1254
A. Yu. Trynin, “On a method for solving a mixed boundary value problem for a parabolic equation using modified sinc-approximation operators”, Comput. Math. Math. Phys., 63:7 (2023), 1264–1284
Dyachenko, MI, “A sharp estimate of the measure of the set of divergence of multiple orthogonal Fourier series”, Studia Mathematica, 159:1 (2003), 33
M. I. Dyachenko, K. S. Kazarian, “On sets of convergence and divergence of multiple orthogonal series”, Sb. Math., 193:9 (2002), 1281–1301
D'yachenko M. Kazaryan K., “Divergence of Multiple Orthogonal Series”, Dokl. Math., 66:1 (2002), 115–117
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