Bernstein widths of some classes of functions defined by a self-adjoint operator. (English) Zbl 1230.41003

Summary: We consider the classes of periodic functions with formal self-adjoint linear differential operators \(W_p(\mathcal L_r)\), which include the classical Sobolev class as its special case. Using the iterative method of Buslaev, we determine with the help of the spectrum of linear differential equations the exact values of Bernstein width of the classes \(W_p(\mathcal L_r)\) in the space \(L_q\) for \(1 < p \leq q < \infty\).


41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
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