Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus

• Published in: Advances in computational mathematics Vol. 50; no. 4
• Main Authors: Liu, Guidong, Liu, Wenjie, Duan, Beiping
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2024; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Estimates; Fractional calculus; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Singularity (mathematics); Sobolev space; Visualization; Jacobi polynomials; Projection error; 41A25; 65N35; Jacobi expansion coefficients; 65M70; 41A10; Generalized Jacobi functions; 41A50; Fractional calculus

In this paper, optimal estimates on the decaying rates of Jacobi expansion coefficients are obtained by fractional calculus for functions with algebraic and logarithmic singularities. This is inspired by the fact that integer-order derivatives fail to deal with singularity of fractional-type, while...