Approximation of functions and quadrature formulas
The method for construction of the new specific base functions is formulated. It is based on the eigenfunctions of the two Sturm-Liouville problems (the operator of the most general kind is the same, but the eigenfunctions are subordinated to two different variants of boundary conditions). The expansion of smooth and piecewise smooth functions by these base functions reduces to rapidly convergent series. This result is a basis for approximation of the above-mentioned set of the functions by a small number of terms.
Note. Abstracts are published in author's edition
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