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What would be the bounds on the derivative of a function using its inverse fourier transform representation. Furthermore what would be the bounds on the absolute value of the function itself?

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You should give more context: where are the functions defined? What is assumed about these one? – Davide Giraudo Sep 25 '12 at 15:30
functions are lipschits having compact support i.e. defined for a bounded interval of real line. – Hafiz ul Asad Sep 25 '12 at 16:06
There are obvious bounds, like bounding the function by the integral of the absolute value of the Fourier transform. However, since that would be the level of homework, you must be looking for something less obvious. I suggest you make your question more precise. Until then, I am voting to close. – Michael Renardy Sep 25 '12 at 17:44
up vote 0 down vote accepted

The standard estimates are $|f(x)|$ is at most the $L^1$ norm of the Fourier transform, and $|f'(x)|$ is at most the first moment of the Fourier transform. Is this what you are asking about?

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i want to know these bounds in terms of some min frequency and max frequency? Can you please have a look at my previous questions?for a system defined by affine vector field, what would be min and max frequency which would bound the value of system trajectory. I am sorry i cant put all this mathematically as i dont know how to enter math expressions here. – Hafiz ul Asad Sep 25 '12 at 21:33
To write mathematical expressions use ordinary TeX commands. After your comments, I don't understand your question at all. You said your function has compact support. Then its Fourier transform is an entire function. So there cannot be any min or max frequency! Frequency spectrum of a function with compact support covers the whole real line. – Alexandre Eremenko Sep 26 '12 at 2:28
In simple words , for all ω∈[0,ω_cuttoff] |L(ω)|≤|F(ω)|≤|U(ω)|, how can we find a relation for this – Hafiz ul Asad Sep 26 '12 at 13:25

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