Question 9.5.5: Consider the equation du/dt = iKu, u(t = 0) = u0, (9.5.126) ...

Linear Algebra and Linear Operators in Engineering: With Applications in Mathematica

Consider the equation

$\frac{du}{dt} = iKu, u(t = 0) = u_{0} ,$ (9.5.126)

where $i = \sqrt{-1}$ and K is a completely continuous, normal operator in H. Assume that the imaginary part of the eigenvalue $\lambda_{n}$ goes as $1 / n^{1/2}$ and examine the asymptotic behavior of u (t).

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