arXiv subjects

Ismail Nikoufar

Publications and source records attributed to Ismail Nikoufar.

7 recordsLinked to original sources

arXiv2025

$L^p$-Theory and Noncommutative Geometry in Quantum Harmonic Analysis

Quantum harmonic analysis extends classical harmonic analysis by integrating quantum mechanical observables, replacing functions with operators and classical convolution structures with their noncommutative counterparts. This paper explores four interrelated developments in this field: (i) a noncommutative $L^p$-theory tailored for quantum harmonic analysis, (ii) the extension of quantum harmonic analysis beyond Euclidean spaces to include Lie groups and homogeneous spaces, (iii) its deep connections with Connes' noncommutative geometry, and (iv) the role of spectral synthesis and approximation properties in quantum settings. We establish novel results concerning the structure and spectral properties of quantum Segal algebras, analyze their functional-analytic aspects, and discuss their implications in quantum physics and operator theory. Our findings provide a unified framework for quantum harmonic analysis, laying the foundation for further advancements in noncommutative analysis and mathematical physics.

math.FA↗

arXiv2022

Mond and Pe$\check{c}$ari$\acute{c}$ inequality for $h$-convex functions with applications

In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type inequality and a multiple operator version of the Jensen's inequality for $h$-convex functions. In particular, a result for convex, $P$-class, $s$-convex, Godunova-Levin, and $s$-Godunova-Levin functions can be deduced.

math.FA↗

arXiv2022

Conditional $h$-convexity with applications

In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's inequality, arithmetic-geometric mean inequality, Chrystal inequality, and H$\ddot{o}$lder-McCarthy inequality. Many of the other inequalities can be refined by applying this new notion.

math.FA↗

arXiv2021

Operator inequalities associated with the Kantrovich type inequalities for $s$-convex functions

In this paper, we prove some operator inequalities associated with an extension of the Kantorovich type inequality for $s$-convex function. We also give an application to the order preserving power inequality of three variables and find a better lower bound for the numerical radius of a positive operator under some conditions.

math.FA↗

arXiv2020

Some inequalities for P-class functions

In this paper, we provide some inequalities for $P$-class functions and self-adjoint operators on a Hilbert space including an operator version of the Jensen's inequality and the Hermite-Hadamard's type inequality. We improve the H\"{o}lder-MacCarthy inequality by providing an upper bound. Some refinements of the Jensen type inequality for $P$-class functions will be of interest.

math.FA↗

arXiv2017

Convexity of parameter extensions of some relative operator entropies with a perspective approach

In this paper, we introduce two notions of a relative operator $(\alpha, \beta)$-entropy and a Tsallis relative operator $(\alpha, \beta)$-entropy as two parameter extensions of the relative operator entropy and the Tsallis relative operator entropy. We apply a perspective approach to prove the joint convexity or concavity of these new notions, under certain conditions concerning $\alpha$ and $\beta$. Indeed, we give the parametric extensions, but in such a manner that they remain jointly convex or jointly concave.

math.FA↗

arXiv2017

Sharp Continuity Bounds for Entropy and Conditional Entropy

The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is derived. This inequality is shown to be tight in the sense that equality can be attained for every prescribed value of the trace norm distance. It includes the sharp Fannes inequality for von Neumann entropy as a special case.

quant-ph↗