K. M. Krishna

We introduce the notion of p-adic equiangular lines and derive the first fundamental relation between common angle, dimension of the space and the number of lines. More precisely,…

math.OA2024

Noncommutative Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani Uncertainty Principle

K. Mahesh Krishna

Let ${τ_{n}}_{n = 1}^{\infty}$ and ${ω_{m}}_{m = 1}^{\infty}$ be two modular Parseval frames for a Hilbert C*-module $E$ . Then for every $x \in E ∖ {0}$ , we sho…

math.FA2024

Continuous Krishna-Parthasarathy Entropic Uncertainty Principle

K. Mahesh Krishna

In 2002, Krishna and Parthasarathy [\textit{Sankhyā Ser. A}] derived discrete quantum version of Maassen-Uffink [\textit{Phys. Rev. Lett., 1988}] entropic uncertainty principle. In…

math.FA2024

Unexpected Uncertainty Principle for Disc Banach Spaces

K. Mahesh Krishna

Let $({f_{n}}_{n = 1}^{\infty}, {τ_{n}}_{n = 1}^{\infty})$ and $({g_{n}}_{n = 1}^{\infty}, {ω_{n}}_{n = 1}^{\infty})$ be unbounded continuous p-Schauder frames ( $0 < p < 1$ ) for a disc Banach space $\…

math.FA2024

Nonlinear Heisenberg-Robertson-Schrodinger Uncertainty Principle

K. Mahesh Krishna

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schr…

math.FA2024

Nonlinear Maccone-Pati Uncertainty Principle

K. Mahesh Krishna

We show that one of the two important uncertainty principles derived by Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary maps defined on subsets of $…

math.FA2024

Functional Kuppinger-Durisi-Bölcskei Uncertainty Principle

K. Mahesh Krishna

Let $X$ be a Banach space. Let ${τ_{j}}_{j = 1}^{n}, {ω_{k}}_{k = 1}^{m} \subseteq X$ and ${f_{j}}_{j = 1}^{n}$ , ${g_{k}}_{k = 1}^{m} \subseteq X^{*}$ satisfy $ |f_j(τ_j)…

math.FA2023

Unbounded Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani Uncertainty Principles

K. Mahesh Krishna

Let $(Ω, μ)$ , $(Δ, ν)$ be measure spaces and $p = 1$ or $p = \infty$ . Let $({f_{α}}_{α \in Ω}, {τ_{α}}_{α \in Ω})$ and $({g_{β}}_{β \in Δ}, {ω_{β}}_{β \in Δ})$ be unbounded continuous p-Sc…

math.FA2023

Continuous Rankin Bound for Hilbert and Banach Spaces

K. Mahesh Krishna

Let $(Ω, μ)$ be a measure space and ${τ_{α}}_{α \in Ω}$ be a normalized continuous Bessel family for a real Hilbert space $H$ . If the diagonal $Δ := {(α, α) : α \in Ω}$ is m…

math.FA2023

Continuous Deutsch Uncertainty Principle and Continuous Kraus Conjecture

K. Mahesh Krishna

Let $(Ω, μ)$ , $(Δ, ν)$ be measure spaces and ${τ_{α}}_{α \in Ω}$ , ${ω_{β}}_{β \in Δ}$ be 1-bounded continuous Parseval frames for a Hilbert space $H$ . Then we show that \be…