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Decomposition Theorems in Non-Commutative Harmonic Analysis
Author: Dr. Alok Nath Tripathy
This paper develops a unified approach to irreducible decomposition theorems within the framework of non-commutative harmonic analysis on locally compact quantum groups. By employing von Neumann algebra techniques, we show that classical Plancherel transform formulas extend naturally to modern quantum settings with quasi-invariant measures.
On Asymptotic Behavior of Solutions to Non-Autonomous Wave Equations
Author: Dr. Elena Rostova
We investigate the qualitative properties and long-time asymptotic behavior of weak solutions to a class of non-autonomous wave equations featuring localized damping terms. Using energy estimates combined with multiplier methods, exponential decay rate bounds are established. Furthermore, we demonstrate the stability of attractors under non-autonomous deterministic perturbations.
Fixed Point Theorems for Generalized Contraction Mappings in Metric Spaces
Author: Prof. Rajesh K. Sharma
In this paper, we establish several novel fixed point theorems for generalized contraction mappings operating within complete metric spaces. We extend the classical Banach contraction principle by introducing a relaxed continuity constraint and proving uniqueness conditions for non-linear operators. Numerical applications to fractional differential equations are presented to illustrate the main theoretical results.
Geometric Properties of Analytic Functions Associated with Conic Domains
Author: Prof. Michael Zhang
The primary aim of this work is to study subclass properties of univalent and analytic functions mapping the unit disk onto generalized conic domains. Sharp coefficient estimates, subordination bounds, and radii of starlikeness are explicitly derived for function classes satisfying differential inequalities.