Some Refinements of Selberg Inequality and Related Results

Abstract

This paper introduces several refinements of the classical Selberg inequality, which isconsidered a significant result in the study of the spectral theory of symmetric spaces, a centraltopic in the field of symmetry studies. By utilizing the contraction property of the Selberg operator,we derive improved versions of the classical Selberg inequality. Additionally, we demonstrate theinterdependence among well-known inequalities such as Cauchy–Schwarz, Bessel, and the Selberginequality, revealing that these inequalities can be deduced from one another. This study showcasesthe enhancements made to the classical Selberg inequality and establishes the interconnectedness ofvarious mathematical inequalities.