8 papers
Jensen-type inequalities on pairs of measure spaces and their applications
Shankhadeep Mondal, P. D. Johnson, R. N. Mohapatra +1
We develop applications of a Jensen-type inequality for pairs of positive measure spaces. The framework yields and operator inequalities for positive integral operators, norm…
Refined upper bounds for the numerical radius via weighted operator means
Shankhadeep Mondal, Ram Narayan Mohapatra, Kasun Tharuka Dewage
We establish a parameterized family of upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space, based on weighted expressions involving the mod…
When Mathematics Meets Painting: Fibonacci Geometry, Cubism and Visual Abstraction
Shankhadeep Mondal, R. N. Mohapatra
This paper explores the Fibonacci sequence and the Golden Ratio as organizing principles for visual composition and abstraction in painting. The author shows how recursive proporti…
Designing optimal dual frames for average error optimization
Shankhadeep Mondal, Deguang Han, R. N. Mohapatra
In this paper, we investigates the problem of optimal dual frame selection for signal reconstruction in the presence of erasures. Unlike traditional approaches relying on left inve…
Optimal K dual frames and pairs in the presence of erasures
Shankhadeep Mondal, Deguang Han, R. N. Mohapatra
This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame…
Optimal Dual Frame Pairs: A Synergy with Graph Theory
Shankhadeep Mondal, Ram Narayan Mohapatra
This paper investigates the optimization of dual frame pairs in the context of erasure problems in data transmission, using a graph theoretical approach. Frames are essential for m…
On the paper Optimal dual frames of probabilistic erasures
Shankhadeep Mondal, Ram Narayan Mohapatra
In the paper Optimal Dual Frames for Probabilistic Erasures, the authors have given conditions under which the canonical dual is claimed to be the unique probability optimal dual f…
Robustness of infinite frames and Besselian structures
Shankhadeep Mondal, Geetika Verma, Ram Narayan Mohapatra
This paper extends the concepts of Minimal Redundancy Condition (MRC) and robustness of erasures for infinite frames in Hilbert spaces. We begin by establishing a comprehensive fra…