Some Refinements of Selberg Inequality and Related Results

被引：5

作者：

Altwaijry, Najla ^{[1
]}

Conde, Cristian ^{[2
,3
]}

Dragomir, Silvestru Sever ^{[4
]}

Feki, Kais ^{[5
,6
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

[2] Natl Sci & Tech Res Council, C1425FQB, Buenos Aires, DF, Argentina

[3] Natl Univ Gen Sarmiento, Sci Inst, JM Gutierrez 1150,B1613GSX, Los Polvorines, Argentina

[4] Victoria Univ, Coll Sport Hlth & Engn, Math, POB 14428, Melbourne, Vic 8001, Australia

[5] Univ Monastir, Fac Econ Sci & Management Mahdia, Mahdia 5111, Tunisia

[6] Univ Sfax, Fac Sci Sfax, Lab Phys Math & Applicat LR 13 ES 22, Sfax 3018, Tunisia

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 08期

关键词：

inner product space; Cauchy-Schwarz inequality; Selberg inequality; orthogonal projection;

D O I：

10.3390/sym15081486

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper introduces several refinements of the classical Selberg inequality, which is considered a significant result in the study of the spectral theory of symmetric spaces, a central topic 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 the interdependence among well-known inequalities such as Cauchy-Schwarz, Bessel, and the Selberg inequality, revealing that these inequalities can be deduced from one another. This study showcases the enhancements made to the classical Selberg inequality and establishes the interconnectedness of various mathematical inequalities.

引用

页数：15

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