Coconvex Approximation by Hybrid Polynomials

We call a hybrid polynomial a function Q ( x ) = α x 2 + β x + T ( x ) , where α , β ∈ R and T is a trigonometric polynomial. For s ≥ 1 , let Y s : = { y i } i ∈ Z , be such that y i + 2 π = y i + 2 s , i ∈ Z . We approximate a function f ( x ) : = g ( x ) + α x 2 , where g is a continuous 2 π -peri...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2022-12, Vol.19 (6), Article 245
Main Authors: Leviatan, D., Motorna, O. V., Shevchuk, I. A.
Format: Article
Language:English
Subjects:
Approximation
Continuity (mathematics)
Inflection points
Mathematical analysis
Mathematics
Mathematics and Statistics
Periodic functions
Polynomials
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Summary:We call a hybrid polynomial a function Q ( x ) = α x 2 + β x + T ( x ) , where α , β ∈ R and T is a trigonometric polynomial. For s ≥ 1 , let Y s : = { y i } i ∈ Z , be such that y i + 2 π = y i + 2 s , i ∈ Z . We approximate a function f ( x ) : = g ( x ) + α x 2 , where g is a continuous 2 π -periodic function and α ∈ R , and f has the collection Y s as its set of inflection points, by hybrid polynomials having the same inflection points. The constant α makes the problem much different than ordinary coconvex trigonometric approximation.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-022-02167-3