We prove that a quadratic matrix of order having complex entries is dichotomic (i.e. its spectrum does not intersect the imaginary axis) if and only if there exists a projection on such that for all and for each real number and each vector the solutions of the following two Cauchy problems are bounded:
Submitted May 29, 2008. Published July 05, 2008.
Math Subject Classifications: 47D06, 35B35.
Key Words: Stable and dichotomic matrices; Cauchy problem; spectral decomposition theorem.
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| Akbar Zada |
Government College University
Abdus Salam School of Mathematical Sciences, (ASSMS)
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