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- W1979920002 abstract "The completely monotonic behavior of the transient responses of RC n-ports to certain pulses of finite duration is used to characterize a more general kind of system, which we call the relaxive Hilbert port. This generalization encompasses networks having an infinite number of lumped and distributed elements as well as an infinite number of ports. A primary result of this work is the generalization of Bernstein’s theorem on completely monotonic functions to operator-valued functions. This in turn leads to a representation theorem, which states that the frequency-domain system function for a relaxive Hilbert port is the Stieltjes transform of a positive-operator measure. The approximation of the unit-impulse response by a finite sum of damped exponentials is discussed. For n-ports, this provides a means of synthesizing a relaxive Hilbert port as an RC network with perhaps ideal transformers. Meixner’s concept of a relaxation system of the second kind is also extended to operator-valued functions, and relaxive Hilbert ports are shown to be special cases of such systems. In fact, relaxive Hilbert ports are precisely those relaxation systems of the second kind whose unit-impulse responses remain bounded. Actually, the inevitable stray capacitances of any physical electrical system force every relaxation system of the second kind to be relaxive. An example of a relaxive infinite system is also given." @default.
- W1979920002 created "2016-06-24" @default.
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- W1979920002 date "1974-02-01" @default.
- W1979920002 modified "2023-10-02" @default.
- W1979920002 title "Relaxive Hilbert Ports" @default.
- W1979920002 doi "https://doi.org/10.1137/0312010" @default.
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