arXiv subjects

Jinyuan Du

Publications and source records attributed to Jinyuan Du.

2 recordsLinked to original sources

arXiv2022

Hilbert Boundary Value Problems for Hyper Monogenic Functions on The Hyperplane

This paper systematically studies Hilbert boundary value problems for hyper monogenic functions on the hyperplane for the solutions being of any integer orders at the infinity, where the negative order cases are new even when restricted to the complex plane context. The explicit solution formulas are given and the solvability conditions are specified. The results are proved through using the Clifford symmetric extension method to reduce Hilbert boundary value problems to Riemann boundary value problems.

math.CV↗

arXiv2008

Orthogonal Trigonometric Polynomials: Riemann-Hilbert Analysis and Relations with OPUC

In this paper, we study the theory of orthogonal trigonometric polynomials (OTP). We obtain asymptotics of OTP with positive and analytic weight functions by Riemann-Hilbert approach and find they have relations with orthogonal polynomials on the unit circle (OPUC). By the relations and the theory of OPUC, we also get four-terms recurrent formulae, Christoffel-Darboux formula and some properties of zeros for orthogonal trigonometric polynomials.

math-ph↗