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


How to Cite

N. E., Mogoi, and Apima S. B. 2023. “Norm-Attainable Polynomials: Characterizations and Properties in Orthogonal Polynomial Families”. Asian Research Journal of Mathematics 19 (10):161-68. https://doi.org/10.9734/arjom/2023/v19i10738.

Downloads

Download data is not yet available.

References

Chatzikonstantinou JA, Nestoridis V. Orthogonal polynomials and norm attaining operators; 2018.

Chihara TS. Introduction to orthogonal polynomials. Gordon and Breach, New York; 1978.

George T. Orthogonal polynomials. TCU Seminar Lecture Notes, Department of Mathematics, Texas Christian University; 2011.

Gorkin P, Laine I. Orthogonal polynomials and norm attainability; 2019.

Mourad EH. Norm attainment for orthogonal polynomials in L2 Spaces. Journal of Approximation Theory. 2019;236.

Yuan Xu. Lecture notes on orthogonal polynomials of several variables. Department of mathematics, University of Oregon Eugene, Oregon 97403-1222, U.S.A.

Zhu K, Zhu Y. Orthogonal polynomials and norm attainment for operators on fock spaces; 2021.