DISCRETE AND CONTINUOUS WELCH BOUNDS FOR BANACH SPACES WITH APPLICATIONS

Authors

K. Mahesh Krishna, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Journal of Classical Analysis

Abstract

In 1974, Welch derived lower bounds (known as Welch bounds) on the maximum of modulus of inner products of distinct elements in a finite collection of unit vectors in a finite dimensional Hilbert space. Recently, continuous Welch bounds are derived for continuous Bessel family of unit vectors indexed over measure spaces in a finite dimensional Hilbert space. In this paper, we derive both discrete and continuous Welch bounds for finite dimensional Banach spaces which contain Welch bounds for finite dimensional Hilbert space case as a particular case. We formulate several problems for future research.

First Page

81

Last Page

111

DOI

https://10.7153/jca-2023-22-07

Publication Date

10-1-2023

Comments

Open Access, Gold

Recommended Citation

Krishna, K. Mahesh, "DISCRETE AND CONTINUOUS WELCH BOUNDS FOR BANACH SPACES WITH APPLICATIONS" (2023). Journal Articles. 3537.
https://digitalcommons.isical.ac.in/journal-articles/3537