Work

Nagy and Pollard-Hilding-Type Stability of Hilbert-Schmidt Frames

Year: 2026

Type: preprint

Abstract: We establish several sufficient conditions ensuring that a perturbed family of operators in a given Hilbert-Schmidt frame for a separable Hilbert space remains a Hilbert-Schmidt frame. The perturbation criteria are formulated through Nagy-type and Pollard-Hilding-type inequalities, yielding explicit estimates for the resulting frame bounds. Several examples are presented to illustrate the applicability of the results.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.22528

Authors: Jyoti, Ruchi, Vashisht, Lalit Kumar

Institution: University of Delhi

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, National Board for Higher Mathematics, University of Delhi

OpenAlex ID: W7214045819

Cites: 1

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Related to: 10