CONTINUOUS WELCH BOUNDS WITH APPLICATIONS

Article Type

Research Article

Publication Title

Communications of the Korean Mathematical Society

Abstract

Let (Ω,μ) be a measure space and {Ƭα}α∈Ω be a normalized continuous Bessel family for a finite dimensional Hilbert space H of dimension d. If the diagonal Δ: = {(α, α): α α∈ Ω} is measurable in the measure space Ω × Ω, then we show that (Formula Presented), ∀m ∈ N. This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

First Page

787

Last Page

805

DOI

https://10.4134/CKMS.c220200

Publication Date

1-1-2023

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