Norm-Attainable Polynomials: Characterizations and Properties in Orthogonal Polynomial Families
Mogoi N. E. *
Kaimosi Friends University, 100, Maragoli, Kenya.
Apima S. B
Kaimosi Friends University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Norm-attainable polynomials play a crucial role in various mathematical contexts. This research paper investigates the characterizations and properties of norm-attainable polynomials in different orthogonal polynomial families. We explore their behavior, convexity, and positive definiteness. Additionally, we establish their norm-attainability in specific intervals for various weight functions. The findings contribute to a deeper understanding of norm-attainable polynomials and their applications in approximation theory and mathematical modeling.
Keywords: Norm-attainable polynomials, orthogonal polynomial families, characterizations, properties