Finding an appropriate function to verify an equation involving a convolution.
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This question is more a reference request, I have never learnt a method (other than by visual inspection) to solve "convolution equations" and wish to know how they are usually dealt with, formally:
Given a real valued function $h$ and a real valued function $f$ what is the mathematical procedure to find a function $g$ s.t.
$$h(t) = int_{- infty}^{infty} f(t- tau) g(tau) d tau$$
real-analysis functional-analysis reference-request
asked Dec 21 '18 at 11:27
MonoliteMonolite
1,5552926
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add a comment |
$begingroup$
This question is more a reference request, I have never learnt a method (other than by visual inspection) to solve "convolution equations" and wish to know how they are usually dealt with, formally:
Given a real valued function $h$ and a real valued function $f$ what is the mathematical procedure to find a function $g$ s.t.
$$h(t) = int_{- infty}^{infty} f(t- tau) g(tau) d tau$$
real-analysis functional-analysis reference-request
asked Dec 21 '18 at 11:27
MonoliteMonolite
1,5552926
$endgroup$
$begingroup$
@drhab so I try various functions $g$ arbitrarily until one satisfies the equation?
$endgroup$
– Monolite
Dec 21 '18 at 11:38
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Sorry, my former comment is wrong (I will delete it). I did not read you question carefully and thought you would be after finding $h$ on base of $f$ and $g$.
$endgroup$
– drhab
Dec 21 '18 at 11:40
1
$begingroup$
Use Fourier transforms and inversion formula, if that works in your example.
$endgroup$
– Kavi Rama Murthy
Dec 21 '18 at 11:45
add a comment |
$begingroup$
This question is more a reference request, I have never learnt a method (other than by visual inspection) to solve "convolution equations" and wish to know how they are usually dealt with, formally:
Given a real valued function $h$ and a real valued function $f$ what is the mathematical procedure to find a function $g$ s.t.
$$h(t) = int_{- infty}^{infty} f(t- tau) g(tau) d tau$$
real-analysis functional-analysis reference-request
asked Dec 21 '18 at 11:27
MonoliteMonolite
1,5552926
$endgroup$
This question is more a reference request, I have never learnt a method (other than by visual inspection) to solve "convolution equations" and wish to know how they are usually dealt with, formally:
Given a real valued function $h$ and a real valued function $f$ what is the mathematical procedure to find a function $g$ s.t.
$$h(t) = int_{- infty}^{infty} f(t- tau) g(tau) d tau$$
real-analysis functional-analysis reference-request
real-analysis functional-analysis reference-request
asked Dec 21 '18 at 11:27
MonoliteMonolite
1,5552926
asked Dec 21 '18 at 11:27
MonoliteMonolite
1,5552926
asked Dec 21 '18 at 11:27
MonoliteMonolite
1,5552926
asked Dec 21 '18 at 11:27
MonoliteMonolite
1,5552926
asked Dec 21 '18 at 11:27
MonoliteMonolite
1,5552926
1,5552926
$begingroup$
@drhab so I try various functions $g$ arbitrarily until one satisfies the equation?
$endgroup$
– Monolite
Dec 21 '18 at 11:38
$begingroup$
Sorry, my former comment is wrong (I will delete it). I did not read you question carefully and thought you would be after finding $h$ on base of $f$ and $g$.
$endgroup$
– drhab
Dec 21 '18 at 11:40
1
$begingroup$
Use Fourier transforms and inversion formula, if that works in your example.
$endgroup$
– Kavi Rama Murthy
Dec 21 '18 at 11:45
add a comment |
$begingroup$
@drhab so I try various functions $g$ arbitrarily until one satisfies the equation?
$endgroup$
– Monolite
Dec 21 '18 at 11:38
$begingroup$
Sorry, my former comment is wrong (I will delete it). I did not read you question carefully and thought you would be after finding $h$ on base of $f$ and $g$.
$endgroup$
– drhab
Dec 21 '18 at 11:40
1
$begingroup$
Use Fourier transforms and inversion formula, if that works in your example.
$endgroup$
– Kavi Rama Murthy
Dec 21 '18 at 11:45
$begingroup$
@drhab so I try various functions $g$ arbitrarily until one satisfies the equation?
$endgroup$
– Monolite
Dec 21 '18 at 11:38
$begingroup$
@drhab so I try various functions $g$ arbitrarily until one satisfies the equation?
$endgroup$
– Monolite
Dec 21 '18 at 11:38
$begingroup$
Sorry, my former comment is wrong (I will delete it). I did not read you question carefully and thought you would be after finding $h$ on base of $f$ and $g$.
$endgroup$
– drhab
Dec 21 '18 at 11:40
$begingroup$
Sorry, my former comment is wrong (I will delete it). I did not read you question carefully and thought you would be after finding $h$ on base of $f$ and $g$.
$endgroup$
– drhab
Dec 21 '18 at 11:40
1
1
$begingroup$
Use Fourier transforms and inversion formula, if that works in your example.
$endgroup$
– Kavi Rama Murthy
Dec 21 '18 at 11:45
$begingroup$
Use Fourier transforms and inversion formula, if that works in your example.
$endgroup$
– Kavi Rama Murthy
Dec 21 '18 at 11:45
add a comment |
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$begingroup$
@drhab so I try various functions $g$ arbitrarily until one satisfies the equation?
$endgroup$
– Monolite
Dec 21 '18 at 11:38
$begingroup$
Sorry, my former comment is wrong (I will delete it). I did not read you question carefully and thought you would be after finding $h$ on base of $f$ and $g$.
$endgroup$
– drhab
Dec 21 '18 at 11:40
1
$begingroup$
Use Fourier transforms and inversion formula, if that works in your example.
$endgroup$
– Kavi Rama Murthy
Dec 21 '18 at 11:45