A Novel Construction of the g-Riesz Decomposition in Hilbert Spaces

Authors

  • Yaling Wang Manzhouli Russian Vocational College

DOI:

https://doi.org/10.55014/pij.v7i3.608

Keywords:

g-framework, g-Riesz decomposition, g-Riesz basis, Riesz basis

Abstract

The concept of the g-frame, a generalized frame in Hilbert spaces, has garnered attention in recent research. While numerous properties of g-frames have been explored, certain aspects remain unexamined, including a novel construction approach for the g-Riesz decomposition in Hilbert spaces. While prior works such as [12] presented the equivalence conditions for g-Riesz decomposition and Khosravi [10] proposed a new construction method for g-frames, neither addressed a new construction method for g-Riesz decomposition. This paper aims to fill this gap by investigating a novel construction method for the specialized g-frame-g-Riesz decomposition. Leveraging operator theory from generalized functional analysis and function space techniques in complex Hilbert spaces, we establish necessary and sufficient conditions for constructing g-Riesz decompositions, an area insufficiently explored by Khosravi and [12]. Furthermore, we introduce two annotations and provide proofs demonstrating that g-Riesz bases are equivalent to Riesz bases, aligning with the findings of W.C. Sun in [6]. This underscores the significance of our research. The newly proposed g-Riesz decomposition not only contributes to mathematical inquiry but also holds promise for various applications, particularly in signal and image processing.

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Published

2024-06-20
CITATION
DOI: 10.55014/pij.v7i3.608
Published: 2024-06-20

How to Cite

Wang, Y. (2024). A Novel Construction of the g-Riesz Decomposition in Hilbert Spaces. Pacific International Journal, 7(3), 11–15. https://doi.org/10.55014/pij.v7i3.608

Issue

Section

Regular