The convolution of two functions, f and g supported on [0,+∞[, under the framework of the Laplace Transform can be writt

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The Convolution Of Two Functions F And G Supported On 0 Under The Framework Of The Laplace Transform Can Be Writt 1 (32.15 KiB) Viewed 34 times

The convolution of two functions, f and g supported on [0,+∞[, under the framework of the Laplace Transform can be written as f∗g=∫−∞+∞​f(t−τ)u(t−τ)g(τ)u(τ)dτ=∫0t​f(t−τ)g(τ)dτ. The Convolution Theorem can be stated as L{f∗g}=F(s)G(s), 5 in which F(s)=L{f} and G(s)=L{g} are the Laplace Transform of f and g, respectively. Use the Convolution Theorem to determine the inverse Laplace Transform of (s2+k2)21​, where k is a real constant.