How can we solve this integral equation for f(t) given g(x) is known?

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The integral equation g(x) = ∫_{-∞}^{∞} dte^{ixf(t)} is presented, where g(x) is known and the goal is to determine the unknown function f(t). The discussion highlights the use of numerical quadrature methods as a potential solution approach. Additionally, participants inquire about the existence of f(t) and whether it can be proven that a solution exists or not. The conversation emphasizes the need for analytical techniques alongside numerical methods to address the problem effectively.

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Karlisbad
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i would need to solve the integral equation..:confused: :confused:

[tex]g(x)=\int_{-\infty}^{\infty}dte^{ixf(t)}[/tex]

the unknown function is f(t) g(x) is known, appart from using a numerical cuadrature method for the integral, what else can i do?.. could we prove if the function f(t) will exist or if it won't have any solution??..thanx.
 
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"the unknown function is f(t) g(x) is known"

*head explodes*
 

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