Akbar Zada
Abstract:
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:
and
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) Lahore, Pakistan email: zadababo@yahoo.com |
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