p-adic Ghobber-Jaming Uncertainty Principle

2025/06/03 by Krishna, K. Mahesh
#11D88 #12J25 #46S10 #47S10 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Information Theory (cs.IT) #Mathematical Physics (math-ph) #Number Theory (math.NT) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2506.18913

Abstract

Let \τ_j\_j=1ⁿ and \ω_k\_k=1ⁿ be two orthonormal bases for a finite dimensional p-adic Hilbert space X. Let M,N⊆ \1, …, n\ be such that max_{j ∈ M, k ∈ N}|⟨ τ_j, ω_k ⟩|lt;1, where o(M) is the cardinality of M. Then for all x ∈ X, we show that (1) ‖x‖≤ (\frac11- max_{j ∈ M, k ∈ N}|⟨ τ_j, ω_k ⟩|)max\ max_{j ∈ M^c}|⟨ x, τ_j⟩ |, max_{k ∈ N^c}|⟨ x, ω_k⟩ |\. We call Inequality (1) as p-adic Ghobber-Jaming Uncertainty Principle. Inequality (1) is the p-adic version of uncertainty principle obtained by Ghobber and Jaming [Linear Algebra Appl., 2011]. We also derive analogues of Inequality (1) for non-Archimedean Banach spaces.

Citations

• p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound

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