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.
Zeroes of rational functions
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rational-functions
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0"The $\;j\omega\;$ axis"? What is that? – 2017-02-02
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0By saying $j\omega$ axis, I mean the imaginary axis in the complex plane. – 2017-02-02
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0But 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. – 2017-02-02
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0@DonAntonio can you please provide a proof for "Any meromorphic non-zero function cannot vanish on any interval". – 2017-02-09