List of top Mathematical Physics Questions on Laplace transforms asked in GATE PH

The solution of Laplace’s equation satisfies which condition?

A function \( f(t) \) is defined only for \( t \geq 0 \). The Laplace transform of \( f(t) \) is \[ \mathcal{L}(f; s) = \int_0^\infty e^{-st} f(t) \, dt \] whereas the Fourier transform of \( f(t) \) is \[ \tilde{f}(\omega) = \int_0^\infty f(t) e^{-i\omega t} \, dt. \] The correct statement(s) is(are)