Work

Uniform and $$L^p$$ Convergence of the Hermite Interpolation at Pollaczek–Laguerre Zeros

Year: 2025

Type: article

Abstract: The paper deals with the weighted polynomial approximation of functions defined on $$(0,+\infty )$$ ( 0 , + ∞ ) , which can grow exponentially both at $$+\infty $$ + ∞ and at 0. To this aim, we introduce interpolating operators of Hermite and Hermite–Fejér-type, based at the zeros of Pollaczek–Laguerre type orthogonal polynomials. We prove that these processes converge in weighted uniform and $$L^p-$$ L p - norms and provide sharp error estimates showing that the order of convergence is the same as the best polynomial approximation, under suitable assumptions.

Source: Mediterranean Journal of Mathematics

DOI: 10.1007/s00009-025-02822-5

Authors: Maria Carmela De Bonis, Giuseppe Mastroianni, Incoronata Notarangelo

Institutions: University of Basilicata, University of Turin

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Università degli Studi di Torino