- #1
klpskp
- 9
- 0
Hello everyone,
I was trying to develop a sort of generalized version of the Fourier Transform. My question in particular is:
Given a function [itex]f(x,u)[/itex], is there a function [itex]g(x,u)[/itex] with [tex]\int_{-\infty}^\infty f(x,u)g(x,u')\mathrm{d}x=\delta(u-u')[/tex]
For [itex]f(x,u)=e^{2\pi ixu}[/itex] the solution would be [itex]g(x,u)=\frac{1}{2\pi}e^{-2\pi ixu}[/itex]. Are there other pairs with this property?
Thank you for your help :)
I was trying to develop a sort of generalized version of the Fourier Transform. My question in particular is:
Given a function [itex]f(x,u)[/itex], is there a function [itex]g(x,u)[/itex] with [tex]\int_{-\infty}^\infty f(x,u)g(x,u')\mathrm{d}x=\delta(u-u')[/tex]
For [itex]f(x,u)=e^{2\pi ixu}[/itex] the solution would be [itex]g(x,u)=\frac{1}{2\pi}e^{-2\pi ixu}[/itex]. Are there other pairs with this property?
Thank you for your help :)