Finite zero-based invariant subspaces of the shift operator on reproducing kernel spaces. Issue 10 (3rd October 2022)

• Record Type: Journal Article
• Authors: Gu, Caixing; Park, Jaehui
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 10(2022)
• Page Start: 2519
• Page End: 2544
• Publication Date: 2022-10-03
• Subjects: Wandering subspace property -- weighted Bergman space -- zero-based invariant subspace -- reproducing kernel space; 47A15 -- 47B32; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.1931850
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : We characterize wandering subspace property of the shift operator on zero-based invariant subspaces of reproducing kernel Hilbert spaces by using the kernels of Toeplitz operators. As applications, we prove that the wandering subspace property of the shift operator holds on the weighted Bergman space A α 2 ( α > 1 ) for zero-based invariant subspaces when the zeros lie in a small disk centred at the origin.