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Widths of classes of periodic differentiable functions in the space \(L_{2} [0, 2\pi]\). (English. Russian original) Zbl 1202.46041
Math. Notes 87, No. 4, 575-581 (2010); translation from Mat. Zametki 87, No. 4, 616-623 (2010).
Summary: We obtain exact values of different \(n\)-widths for classes of differentiable periodic functions in the space \(L_{2}[0,2\pi]\) satisfying the constraint \[ \left({\int_0^h{\omega_m^p\left({f^{\left(r\right)};t}\right)\,dt}}\right)^{1/p}\leqslant\Phi\left(h\right), \] where \(0<h<\infty\), \(1/r<p\leq 2\), \(r\in\mathbb N\), and \(\omega_m(f^{(r)};t)\) is the modulus of continuity of \(m\)th order of the derivative \(f^{(r)}(x)\in L_{2}[0,2\pi]\).

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
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