On an atomic decomposition in Banach spaces

Abstract

An atomic decomposition is considered in Banach space. A method for constructing an atomic decomposition of Banach space, starting with atomic decomposition of subspaces is presented. Some relations between them are established. The proposed method is used in the study of the frame properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

Keywords

• $p$-frames
• $tilde{X}$-frames
• Conjugate systems to $tilde{X}$