Fourier and Laplace transforms together, is this possible?

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Answering on some posts on MSE about Laplace transform and Fourier transform I stumbled upon a question to which I cannot answer myself (not having a good ground in pure mathematics).



The question is the following:




Is there some mathematical constraint that doesn't let us use both Fourier and Laplace transform on the same equation?




I'm not saying that it would be useful in any case, I was just wondering if it's feasible! Just as an example I could use both transforms to solve the one dimensional (or three, doesn't change much) wave equation with some external force $$begincasespartial^2_tu(x,t) - c^2partial^2_xu(x,t) = f(x,t)\u(x,0) = partial_tu(x,t)|_t=0=0\-inftylt xltinfty;;;;tgt0endcases$$




pde fourier-analysis laplace-transform fourier-transform




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  • 1




    You can use both as any times as makes sense. The two transforms are very similar in nature and the multidimensional versions are just iterated one dimensional transforms. A long winded way of saying yes.
    – copper.hat
    2 hours ago











  • Thanks! If you want, write it as an answer
    – Davide Morgante
    2 hours ago














up vote
1
down vote

favorite












Answering on some posts on MSE about Laplace transform and Fourier transform I stumbled upon a question to which I cannot answer myself (not having a good ground in pure mathematics).



The question is the following:




Is there some mathematical constraint that doesn't let us use both Fourier and Laplace transform on the same equation?




I'm not saying that it would be useful in any case, I was just wondering if it's feasible! Just as an example I could use both transforms to solve the one dimensional (or three, doesn't change much) wave equation with some external force $$begincasespartial^2_tu(x,t) - c^2partial^2_xu(x,t) = f(x,t)\u(x,0) = partial_tu(x,t)|_t=0=0\-inftylt xltinfty;;;;tgt0endcases$$




pde fourier-analysis laplace-transform fourier-transform




share|cite|improve this question

















  • 1




    You can use both as any times as makes sense. The two transforms are very similar in nature and the multidimensional versions are just iterated one dimensional transforms. A long winded way of saying yes.
    – copper.hat
    2 hours ago











  • Thanks! If you want, write it as an answer
    – Davide Morgante
    2 hours ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Answering on some posts on MSE about Laplace transform and Fourier transform I stumbled upon a question to which I cannot answer myself (not having a good ground in pure mathematics).



The question is the following:




Is there some mathematical constraint that doesn't let us use both Fourier and Laplace transform on the same equation?




I'm not saying that it would be useful in any case, I was just wondering if it's feasible! Just as an example I could use both transforms to solve the one dimensional (or three, doesn't change much) wave equation with some external force $$begincasespartial^2_tu(x,t) - c^2partial^2_xu(x,t) = f(x,t)\u(x,0) = partial_tu(x,t)|_t=0=0\-inftylt xltinfty;;;;tgt0endcases$$




pde fourier-analysis laplace-transform fourier-transform




share|cite|improve this question













Answering on some posts on MSE about Laplace transform and Fourier transform I stumbled upon a question to which I cannot answer myself (not having a good ground in pure mathematics).



The question is the following:




Is there some mathematical constraint that doesn't let us use both Fourier and Laplace transform on the same equation?




I'm not saying that it would be useful in any case, I was just wondering if it's feasible! Just as an example I could use both transforms to solve the one dimensional (or three, doesn't change much) wave equation with some external force $$begincasespartial^2_tu(x,t) - c^2partial^2_xu(x,t) = f(x,t)\u(x,0) = partial_tu(x,t)|_t=0=0\-inftylt xltinfty;;;;tgt0endcases$$





pde fourier-analysis laplace-transform fourier-transform





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 3 hours ago









Botond

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asked 4 hours ago









Davide Morgante

1,566118




1,566118







  • 1




    You can use both as any times as makes sense. The two transforms are very similar in nature and the multidimensional versions are just iterated one dimensional transforms. A long winded way of saying yes.
    – copper.hat
    2 hours ago











  • Thanks! If you want, write it as an answer
    – Davide Morgante
    2 hours ago












  • 1




    You can use both as any times as makes sense. The two transforms are very similar in nature and the multidimensional versions are just iterated one dimensional transforms. A long winded way of saying yes.
    – copper.hat
    2 hours ago











  • Thanks! If you want, write it as an answer
    – Davide Morgante
    2 hours ago







1




1




You can use both as any times as makes sense. The two transforms are very similar in nature and the multidimensional versions are just iterated one dimensional transforms. A long winded way of saying yes.
– copper.hat
2 hours ago





You can use both as any times as makes sense. The two transforms are very similar in nature and the multidimensional versions are just iterated one dimensional transforms. A long winded way of saying yes.
– copper.hat
2 hours ago













Thanks! If you want, write it as an answer
– Davide Morgante
2 hours ago




Thanks! If you want, write it as an answer
– Davide Morgante
2 hours ago















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