Abstract
An impulse response f (with support on the nonnegative real numbers) is said to be in A_ if, on í t ≥ 0,f(t) = f a (t) + f sa (t) where its regular functional part f a is such that \( \int_0^\infty {|f\left( t \right)|} \;exp \left( { - \sigma t} \right)dt < \infty \) and its singular atomic part \( {f_{sa}}: = \sum\nolimits_{i = 0}^\infty {f\delta \left( {. - {t_i}} \right),} \) where t o = 0,t i > 0 for i ≥ 1 and f i ∈ ℂ for i ≥ 0 with \(\sum\nolimits_{{i = 0}}^{\infty } {|f\left( t \right)|\exp \left( { - \sigma {{t}_{i}}} \right) < \infty } ,\) for some σ < 0. Â_ denotes the algebra of distributed parameter system proper-stable transfer functions, i.e. Laplace transforms of elements in A_.
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© 1999 Springer-Verlag London Limited
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Callier, F.M., Winkin, J.J. (1999). Spectral factorization of a spectral density with arbitrary delays. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_17
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DOI: https://doi.org/10.1007/978-1-4471-0807-8_17
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