Generalized lyapunov equations and positive definite functions

SIAM Journal on Matrix Analysis and Applications

Volumn 27, Issue 1, 2006, Pages 103-114

  Bhatia, Rajendra ^a   Drissi, Driss ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b KUWAIT UNIVERSITY   (Kuwait)

Author keywords

Bochner's theorem; Fourier transform; Lyapunov matrix equation; Operator means; Positive definite function; Positive definite matrix

Indexed keywords

FOURIER TRANSFORMS; LINEAR EQUATIONS; MATRIX ALGEBRA; THEOREM PROVING;

BOCHNER'S THEOREM; LYAPUNOV MATRIX EQUATION; OPERATOR MEANS; POSITIVE DEFINITE FUNCTION; POSITIVE DEFINITE MATRIX;

LYAPUNOV METHODS;

EID: 33144478296     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/040608970     Document Type: Article

References (15)

1. R. BHATIA, Matrix Analysis, Springer-Verlag, New York, 1997.
2. R. BHATIA AND C. DAVIS, More matrix forms of the arithmetic-geometric mean inequality, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 132-136.
3. R. BHATIA AND F. KITTANEH, On the singular values of a product of operators, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 272-277.
4. R. BHATIA AND K. R. PARTHASARATHY, Positive definite functions and operator inequalities, Bull. London Math. Soc., 32 (2000), pp. 214-228.
5. S. K. GODUNOV, Modern Aspects of Linear Algebra, Transl. Math. Monogr. 175, AMS, Providence, RI, 1998.
6. E. HEINZ, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann., 123 (1951), pp. 415-438.
7. F. HIAI AND H. KOSAKI, Comparison of various means for operators, J. Funct. Anal., 163 (1999), pp. 300-323.
8. F. HIAI AND H. KOSAKI, Means of matrices and comparison of their norms, Indiana Univ. Math. J., 48 (1999), pp. 899-936.
9. F. HIAI AND H. KOSAKI, Means of Hilbert Space Operators, Lecture Notes in Math. 1820, Springer-Verlag, Berlin, 2003.
10. R. A. HORN AND C. R. JOHNSON, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1990.
11. H. KOSAKI, Arithmetic-geometric mean and related inequalities for operators, J. Funct. Anal., 156 (1998), pp. 429-451.
12. M. K. KWONG, On the definiteness of the solutions of certain matrix equations, Linear Algebra Appl., 108 (1988), pp. 177-197.
13. A. M. LYAPUNOV, The General Problem of the Stability of Motion, English translation, Taylor and Francis, London, 1992.
14. D. S. MITRINOVIC AND J. D. KECKIC, The Cauchy Method of Residues, D. Reidel, Dordrecht, The Netherlands, 1984.
15. X. ZHAN, Inequalities for unitarily invariant norms, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 466-470.