I am reading upon the rational functions and came across this question.
How to prove that a rational function F(s) cannot be zero on any interval on the $j\omega$ axis?
By intuition, we can say that a rational function can have only a finite number of zeros.But how to prove this.
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Manideep
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"The $;j\omega;$ axis"? What is that? – DonAntonio Feb 02 '17 at 15:52
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By saying $j\omega$ axis, I mean the imaginary axis in the complex plane. – Manideep Feb 02 '17 at 17:15
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But then the above is true not only for rational function but for any meromorphic non-zero function: it cannot vanish on any interval of positive length on any axis or whatever. – DonAntonio Feb 02 '17 at 18:09
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@DonAntonio can you please provide a proof for "Any meromorphic non-zero function cannot vanish on any interval". – Manideep Feb 09 '17 at 02:03