Bochner PG-Frames
Morteza Rahmani, Mohammad H. Faroughi
TL;DR
This paper introduces Bochner pg-frames for Banach spaces, characterizes their properties, explores their relation to Bochner qg-Riesz bases, and discusses their stability under perturbations.
Contribution
It is the first to define and analyze Bochner pg-frames, including bounds, basis relations, and perturbation effects in Banach spaces.
Findings
Characterized Bochner pg-frames and their optimal bounds.
Established relations between Bochner pg-frames and Bochner qg-Riesz bases.
Discussed stability of Bochner pg-frames under perturbations.
Abstract
In this paper we introduce the concept of Bochner pg-frames for Banach spaces. We characterize the Bochner pg-frames and specify the optimal bounds of a Bochner pg- frames. Then we define a Bochner qg-Riesz basis and verify the relations between Bochner pg-frames and Bochner qg-Riesz bases. Finally, we discuss the perturbation of Bochner pg-frames.
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Taxonomy
TopicsMathematical Analysis and Transform Methods