NEW PROOFS AND A GENERALIZATION OF INEQUALITIES OF FAN, TAUSSKY, AND TODD

Journal article

Discrete Fourier analysis is used to obtain simple proofs of certain inequalities about finite number sequences determined by Fan, Taussky, and Todd [Monatsh. Math. 59 (1955), 73-90] and their converses determined by Milovanović and Milovanović [J. Math., Anal. Appl.88 (1992), 378-387]. Using the same techniques, the inequality [formula] is proved for all real numbers 0=b0, b1, ..., bn, bn+1=0, which answers a question raised by Alzer [J. Math. Anal. Appl.161 (1991), 142-147]. Second, the method is used to obtain the eigenvalues and eigenvectors of matrices (aij) that are rotation-invariant, i.e., that obey (aij)=(a(i+1)(j+1)). © 1994 Academic Press. All rights reserved.

Authors: Lunter, G

• Publication status: Published
• Journal: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
• Volume: 185
• Issue: 2
• Pages: 464-476
• Publication date: 1994-07-15
• DOI: 10.1006/jmaa.1994.1261
• EISSN: 1096-0813
• ISSN: 0022-247X