Associative property of convolution

Click For Summary
SUMMARY

The discussion centers on proving the associative property of convolution for finite intervals, contrasting with established proofs for infinite intervals. Aman Integral's approach was criticized for incorrectly using the variable \(\theta\) in the bounds of integrals. Micromass suggested applying the Fubini theorem correctly after equation (9) to resolve the issue. The need for resources on the Fubini theorem in the context of variable bounds was also highlighted.

PREREQUISITES
  • Understanding of convolution properties in mathematics
  • Familiarity with the Fubini theorem and its applications
  • Knowledge of finite and infinite interval integration
  • Basic skills in mathematical proof techniques
NEXT STEPS
  • Research the Fubini theorem and its implications for variable bounds in integration
  • Study the properties of convolution in finite intervals
  • Examine mathematical proofs related to the associative property of convolution
  • Explore advanced integration techniques and their applications in analysis
USEFUL FOR

Mathematicians, students studying analysis, and anyone interested in advanced integration techniques and convolution properties.

sainistar
Messages
3
Reaction score
0
Hi There

The associative property of convolution is proved in literature for infinite interval. I want to prove the associative property of convolution for finite interval. I have explained the problem in the attached pdf file.

Any help is appreciated.

Regards
Aman
 

Attachments

Physics news on Phys.org
Integral (10) is obviously wrong. Your two integrals have [itex]\theta[/itex] in their bounds. But [itex]\theta[/itex] is an integration variable! This can't be correct.

Why do you obtain something wrong here. Because after equation (3) they applied Fubini and switched the both integrals, and THEN they did the substitution.

You must do something similar. Apply Fubini after (9). But Fubini will in this case not be simply switching the integral signs...
 
Thanks micromass

I was looking for the Fubini theorem when the bound are the integration variable. I did not find any. Can you please let me know any source i can read.
It will also be helpful if you can suggest how can i apply Fubini after (9).

Regards
 

Similar threads

Semigroup property for convolution
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Integral of Dirac function from 0 to a.... value
  • · Replies 3 ·
Replies
3
Views
2K
Can the Least Squares Method be expressed as a convolution?
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Problem in Convolution integral by fourier transformation
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Differentiation with convolution operators
  • · Replies 1 ·
Replies
1
Views
3K
Engineering How to find the impulse function?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Convolution - calculation and drawing
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How Do You Compute the Convolution of a Convolution with Variable Limits?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad The differences between autocorrelation and convolution
  • · Replies 4 ·
Replies
4
Views
10K
Undergrad Group like operations that are not associative
  • · Replies 3 ·
Replies
3
Views
3K