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Results tagged with fourier-transform
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user 4362
21
votes
Accepted
Where does the Laplace transform come from?
Set $A = L^1([0, \infty))$, equipped with the structure of a Banach $*$-algebra via convolution. The spectrum of this algebra is the half plane $\text{Re}(z) \geq 0$, and the Gelfand transform is the …
- 29.2k
2
votes
Is there (fast) fourier transform for vector convolution?
I think this all falls out of general nonsense with group algebras. Given a locally compact group $G$ there is a homomorphism of Banach algebras $\mathcal{F} \colon L^1(G) \to C_0(\hat{G})$ where:
…
- 29.2k