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Necessary and sufficient nonnegativity conditions for second-order coordinate trigonometric splines. (English. Russian original) Zbl 1384.41006

Vestn. St. Petersbg. Univ., Math. 50, No. 1, 5-10 (2017); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 62, No. 1, 9-16 (2017).
Summary: Necessary and sufficient nonnegativity conditions for continuous differentiable coordinate trigonometric splines of the second order are obtained; the convexity and concavity intervals of these splines are determined. The method of investigation consists in recognizing concavity in intervals adjacent to the endpoints of the support of a coordinate spline under consideration and applying arguments related to the number of zeros of the solution of the corresponding boundary value problem for a second-order differential equation.

MSC:

41A15 Spline approximation
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