Necessary and sufficient nonnegativity conditions for second-order coordinate trigonometric splines

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 adjacen...

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Bibliographic Details
Published in:Vestnik, St. Petersburg University. Mathematics St. Petersburg University. Mathematics, 2017, Vol.50 (1), p.5-10
Main Authors: Dem’yanovich, Yu. K., Makarov, A. A.
Format: Article
Language:English
Subjects:
Analysis
Boundary value problems
Concavity
Convexity
Differential equations
Intervals
Mathematics
Mathematics and Statistics
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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.
ISSN:1063-4541
1934-7855
DOI:10.3103/S1063454117010034