Polynomial interpolation and residue currents. Issue 7 (3rd July 2022)

• Record Type: Journal Article
• Authors: Johansson, Jimmy
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 7(2022)
• Page Start: 1772
• Page End: 1781
• Publication Date: 2022-07-03
• Subjects: Polynomial interpolation -- residue currents -- moment conditions -- Hermite interpolation; 32A27 -- 32C30; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.1897796
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : We show that a global holomorphic section of O ( d ) restricted to a closed complex subspace X ⊂ P n has an interpolant if and only if it satisfies a set of moment conditions that involves a residue current associated with a locally free resolution of O X . When X is a finite set of points in C n ⊂ P n this can be interpreted as a set of linear conditions that a function on X has to satisfy in order to have a polynomial interpolant of degree at most d .