Is there any close-form solution for a function $f(t)$ satisfied the below equation: $f(t)=g(t)+\frac{1}{t^2}(h(t)*f(t))$. Operator $*$ is convolution integral, and $g(t)$ and $h(t)$ are known functions.
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2$\begingroup$ Please provide more detail, for example what class of functions are you considering? Measurable? Smooth? C^1? Schwarz? etc $\endgroup$– David Roberts ♦Jul 8, 2013 at 10:56
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1$\begingroup$ On that set $f$ is defined? $\endgroup$– AndrewJul 8, 2013 at 11:11
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$\begingroup$ $t>0$ and is a real value. At the first, we have no condition on $f$. $\endgroup$– Venous007Jul 8, 2013 at 12:10
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$\begingroup$ And what is a "closed form"? A formula with Fourier transforms and convolutions is a "closed form" or not? $\endgroup$– Alexandre EremenkoJul 8, 2013 at 22:13
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1$\begingroup$ I think you should give explicitly $g$ and $h$. For $t\ne 0$, a Fourier transform of this equation gives $f''(\omega)+h(\omega)f(\omega)=g''(\omega)$ that has known solutions just for some special cases of h. $\endgroup$– JonJul 9, 2013 at 12:41
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