No Laplace Transform? What can be said about the function?

AI Thread Summary
A function that lacks a Laplace transform does not necessarily imply a specific characteristic about its behavior or properties, unlike the clear connection between the absence of a Fourier transform and infinite energy. The Laplace transform is primarily a tool used in engineering to transition between time and frequency domains. While convolution in the time domain corresponds to multiplication in the frequency domain, the absence of a Laplace transform does not directly indicate a fundamental issue with the function itself. The discussion highlights confusion regarding the relationship between Laplace transforms and other mathematical concepts, such as Fourier series and Dirichlet conditions. Ultimately, there is no clear theoretical implication for functions without a Laplace transform.
hadron23
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Hi,

We know that if a function does not have a Fourier transform, then it does not have finite energy. Is there an equivalent intuition associated with a function that does not have a Laplace transform?
 
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hadron23 said:
Hi,

We know that if a function does not have a Fourier transform, then it does not have finite energy. Is there an equivalent intuition associated with a function that does not have a Laplace transform?

Could you provide a link to your first assertion please?
 
berkeman said:
Could you provide a link to your first assertion please?

Alright, I think I got confused with something to do with Fourier Series (not transform) and Dirichlet conditions. Nevermind that first statement. The question is, what can be said about the function, if it does not have a Laplace transform?
 
Laplace Transform is just a means engineers convert representations in time domain into frequency domains in engineering. Things in time domain do happen in frequency domain. as F= 1/T. Convolution (which is complicated) in the time domain means multiplication in the frequency domain - which helps things out.

Not too sure there is any existence between if a function has no laplace means other theory.
 

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