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Estimates for wavelet coefficients on some classes of functions
Let ψmD be orthogonal Daubechies wavelets that have m zero moments and let {fx1791-01}. We prove that {fx1791-02}.
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Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions
AbstractFor certain classes of functions (all functions are defined on a Jordan measurable set G) defined by a majorant on the modulus of continuity, we find an asymptotically sharp bound for theExpand
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On the Optimal Recovery of Integrals of Set-Valued Functions
We consider the problem of optimization of the approximate integration of set-valued functions from the class specified by a given majorant of their moduli of continuity performed by using the valuesExpand
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Approximation of Some Classes of Set-Valued Periodic Functions by Generalized Trigonometric Polynomials
We generalize some known results on the best, best linear, and best one-sided approximations by trigonometric polynomials from the classes of 2π-periodic functions represented in the form ofExpand
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Widths and optimal quadrature formulas for convolution classes
We compute Kolmogorov widths in the space L1 for classes of periodic functions representable in the form of a kernel convolution that does not increase the number of sign changes with values in aExpand
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The best L1-approximations of classes of functions defined by differential operators in terms of generalized splines from these classes
For classes of periodic functions defined by constraints imposed on the L1-norm of the result of action of differential operators with constant coefficients and real spectrum on these functions, weExpand
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On optimization of weight quadrature formulas
We obtain asymptotically optimal quadrature formulas on the classHω[-1, 1] for an arbitrary continuous weight function which is positive on [-1, 1] almost everywhere and for a wide class of moduli ofExpand
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