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Jan
29
awarded  Supporter
Jan
9
comment Convergence of $\lim \limits_{n,v \rightarrow \infty} \int_0^1 F_n (x) e^{-i2\pi v x} \mbox{d} x $
Thanks TCL, I changed the condition.
Jan
9
revised Convergence of $\lim \limits_{n,v \rightarrow \infty} \int_0^1 F_n (x) e^{-i2\pi v x} \mbox{d} x $
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Jan
4
revised Convergence of $\lim \limits_{n,v \rightarrow \infty} \int_0^1 F_n (x) e^{-i2\pi v x} \mbox{d} x $
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Jan
4
comment Convergence of $\lim \limits_{n,v \rightarrow \infty} \int_0^1 F_n (x) e^{-i2\pi v x} \mbox{d} x $
If $n$ and $v$ goes to infinity at the same rate (which I should include in the conditions), that limit exists.
Jan
2
comment Convergence of $\lim \limits_{n,v \rightarrow \infty} \int_0^1 F_n (x) e^{-i2\pi v x} \mbox{d} x $
@TCL, That simple case has been answered by Nick Kirby in the question [Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $] linked above.
Jan
1
awarded  Student
Jan
1
asked Convergence of $\lim \limits_{n,v \rightarrow \infty} \int_0^1 F_n (x) e^{-i2\pi v x} \mbox{d} x $
Jan
1
awarded  Scholar
Jan
1
accepted Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $
Dec
31
comment Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $
Yes I see your point, just mis-understood you.
Dec
31
comment Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $
My feeling is, if $v/n$ is not integer, integration of the product $f_n(x)e^{-i2\pi v x}$ cannot be broken into a sum of $n$ integrals. Can you give more hints?
Dec
31
comment Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $
It is the convergence in the two variables simultaneously.
Dec
31
revised Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $
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Dec
31
revised Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $
added 12 characters in body; added 26 characters in body; edited title
Dec
30
awarded  Editor
Dec
30
revised Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $
added 1 characters in body; edited title
Dec
30
revised Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $
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Dec
30
asked Convergence of $\lim_{n,v \rightarrow \infty} \int_0^1 f_n (x) e^{-i2\pi v x} \mbox{d} x $