K. M. Krishna

activity

20182023

most citedDiscrete and Continuous Welch Bounds for Banach Spaces with Applications

14 citations · 56 across the 37 of their papers we have counts for

collaborators

41 papers

math.FA2023★ 2 cited

Functional Deutsch Uncertainty Principle

K. Mahesh Krishna

Let ${f_{j}}_{j = 1}^{n}$ and ${g_{k}}_{k = 1}^{m}$ be Parseval p-frames for a finite dimensional Banach space $X$ . Then we show that \begin{align} (1) \quad\quad\quad\quad \log…

math.FA2023

Functional Continuous Uncertainty Principle

K. Mahesh Krishna

Let $(Ω, μ)$ , $(Δ, ν)$ be measure spaces. Let $({f_{α}}_{α \in Ω}, {τ_{α}}_{α \in Ω})$ and $({g_{β}}_{β \in Δ}, {ω_{β}}_{β \in Δ})$ be continuous p-Schauder frames for a Banach space $…

math.FA2023

Functional Donoho-Stark Approximate Support Uncertainty Principle

K. Mahesh Krishna

Let $({f_{j}}_{j = 1}^{n}, {τ_{j}}_{j = 1}^{n})$ and $({g_{k}}_{k = 1}^{n}, {ω_{k}}_{k = 1}^{n})$ be two p-orthonormal bases for a finite dimensional Banach space $X$ . If $ x \in \mathca…

math.FA2023

Functional Ghobber-Jaming Uncertainty Principle

K. Mahesh Krishna

Let $({f_{j}}_{j = 1}^{n}, {τ_{j}}_{j = 1}^{n})$ and $({g_{k}}_{k = 1}^{n}, {ω_{k}}_{k = 1}^{n})$ be two p-orthonormal bases for a finite dimensional Banach space $X$ . Let $M,N\subseteq…

math.FA2023★ 1 cited

Group-Frames for Banach Spaces

K. Mahesh Krishna

In the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach space…

math.FA2023★ 5 cited

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

K. Mahesh Krishna

Let $({f_{j}}_{j = 1}^{n}, {τ_{j}}_{j = 1}^{n})$ and $({g_{k}}_{k = 1}^{m}, {ω_{k}}_{k = 1}^{m})$ be p-Schauder frames for a finite dimensional Banach space $X$ . Then for every $x \in \m…

math.FA2023

Absolutely Summing Morphisms between Hilbert C*-Modules and Modular Pietsch Factorization Problem

K. Mahesh Krishna

Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom \textit{[J. Funct. Anal., 2021]}, we intro…

math.FA2023

Localized Bounded Below Approximate Schauder Frames are Finite Unions of Approximate Riesz Sequences

K. Mahesh Krishna

Based on the truth of Feichtinger conjecture by Marcus, Spielman and Srivastava \textit{[Ann. of Math. (2), 2015]} and from the localized version by Gröchenig \textit{[Adv. Comput.…

math.FA2022

Lipschitz p-Approximate Schauder Frames

K. Mahesh Krishna, P. Sam Johnson

With the aim of representing subsets of Banach spaces as an infinite series using Lipschitz functions, we study a variant of metric frames which we call Lipschitz p-approximate Sch…

cs.IT2022

Non-Archimedean Welch Bounds and Non-Archimedean Zauner Conjecture

K. Mahesh Krishna

Let $K$ be a non-Archimedean (complete) valued field satisfying \begin{align*} \left|\sum_{j=1}^{n}λ_j^2\right|=\max_{1\leq j \leq n}|λ_j|^2, \quad \forall λ_j \in \mathbb…

math.NT2022

p-adic Magic Contractions, p-adic von Neumann Inequality and p-adic Sz.-Nagy Dilation

K. Mahesh Krishna

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic…

math.NT2022

Continuous Non-Archimedean and p-adic Welch Bounds

K. Mahesh Krishna

We prove the continuous non-Archimedean (resp. p-adic) Banach space and Hilbert space versions of non-Archimedean (resp. p-adic) Welch bounds proved by M. Krishna. We formulate con…

math.NT2022

Non-Archimedean and p-adic Functional Welch Bounds

K. Mahesh Krishna

We prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following…

math.FA2022

Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Johnson-Lindenstrauss Flattening Conjecture

K. Mahesh Krishna

We recently formulated important Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Modular Johnson-Lindenstrauss Flattening Conjecture in the Appendix of \textit{[…

math.FA2022★ 4 cited

Modular Paulsen Problem and Modular Projection Problem

K. Mahesh Krishna

Based on the solution of \textbf{Paulsen Problem} by Kwok, Lau, Lee, and Ramachandran [\textit{STOC'18-Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2…

math.FA2022★ 4 cited

C*-algebraic Casas-Alvero Conjecture

K. Mahesh Krishna

Based on Casas-Alvero conjecture \textit{[J. Algebra, 2001]} we formulate the following conjecture.\\ \textbf{C*-algebraic Casas-Alvero Conjecture : Let $A$ be a commutat…

math.FA2022★ 4 cited

C*-algebraic Smale Mean Value Conjecture and Dubinin-Sugawa Dual Mean Value Conjecture

K. Mahesh Krishna

Based on Smale mean value conjecture \textit{[Bull. Amer. Math. Soc., 1981]} and Dubinin-Sugawa dual mean value conjecture \textit{[Proc. Japan Acad. Ser. A Math. Sci., 2009]} we f…

math.OA2022★ 4 cited

C*-algebraic Schoenberg Conjecture

K. Mahesh Krishna

Based on Schoenberg conjecture \textit{[Amer. Math. Monthly., 1986]}/Malamud-Pereira theorem \textit{[J. Math. Anal. Appl, 2003]}, \textit{[Trans. Amer. Math. Soc., 2005]} we formu…

math.FA2022

Metric, Schauder and Operator-Valued Frames

K. Mahesh Krishna

Notion of frames and Bessel sequences for metric spaces have been introduced. This notion is related with the notion of Lipschitz free Banach spaces. \ It is proved that every sepa…

math.FA2022

The $(ab c, pq r)$ -problem for Approximate Schauder Frames for Banach Spaces

K. Mahesh Krishna

Motivated from the complete solution of important $ab c$ -problem for Gabor system for the Hilbert space $L^{2} (R)$ by Dai and Sun [\textit{Memoirs of Amer. Math. So…

math.FA2022

Operator-Valued p-Approximate Schauder Frames

K. Mahesh Krishna, P. Sam Johnson

We give an operator-algebraic treatment of theory of p-approximate Schuader frames which includes the theory of operator-valued frames by Kaftal, Larson, and Zhang [\textit{Trans.…

math.FA2022

Paulsen and Projection Problems for Banach Spaces

K. Mahesh Krishna

Based on the two decades old celebrated Paulsen problem and its solutions for Hilbert spaces by Kwok, Lau, Lee, Ramachandran, Hamilton, and Moitra, we formulate Paulsen problem for…

math.FA2022★ 14 cited

Discrete and Continuous Welch Bounds for Banach Spaces with Applications

K. Mahesh Krishna

Let ${τ_{j}}_{j = 1}^{n}$ be a collection in a finite dimensional Banach space $X$ of dimension $d$ and ${f_{j}}_{j = 1}^{n}$ be a collection in $X^{*}$ (dual of $\mathca…

math.OA2022★ 13 cited

Modular Welch Bounds with Applications

K. Mahesh Krishna

We prove the following two results. \begin{enumerate} \item Let $A$ be a unital commutative C*-algebra and $A^{d}$ be the standard Hilbert C*-module over $\mathca…

Functional Deutsch Uncertainty Principle

Functional Continuous Uncertainty Principle

Functional Donoho-Stark Approximate Support Uncertainty Principle

Functional Ghobber-Jaming Uncertainty Principle

Group-Frames for Banach Spaces

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

Absolutely Summing Morphisms between Hilbert C*-Modules and Modular Pietsch Factorization Problem

Localized Bounded Below Approximate Schauder Frames are Finite Unions of Approximate Riesz Sequences

Lipschitz p-Approximate Schauder Frames

Non-Archimedean Welch Bounds and Non-Archimedean Zauner Conjecture

p-adic Magic Contractions, p-adic von Neumann Inequality and p-adic Sz.-Nagy Dilation

Continuous Non-Archimedean and p-adic Welch Bounds

Non-Archimedean and p-adic Functional Welch Bounds

Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Johnson-Lindenstrauss Flattening Conjecture

Modular Paulsen Problem and Modular Projection Problem

C*-algebraic Casas-Alvero Conjecture

C*-algebraic Smale Mean Value Conjecture and Dubinin-Sugawa Dual Mean Value Conjecture

C*-algebraic Schoenberg Conjecture

Metric, Schauder and Operator-Valued Frames

The (abc,pqr)-problem for Approximate Schauder Frames for Banach Spaces

Operator-Valued p-Approximate Schauder Frames

Paulsen and Projection Problems for Banach Spaces

Discrete and Continuous Welch Bounds for Banach Spaces with Applications

Modular Welch Bounds with Applications

The $(ab c, pq r)$ -problem for Approximate Schauder Frames for Banach Spaces