If taking this operator on a function f of x yields big f of y, taking this operator on f of a times x yields one over a times big f of quantity y over a according to its "scaling property."
If taking this operator on a function f of x yields big f of y, taking this operator on f of a times x yields one over a times big f of quantity y over a according to its "scaling property." The inverse of this operator on a function is equal to one over 2 pi i times the integral from gamma minus i times infinity to gamma plus i times infinity of this operator's kernel times the function. Taking this operator on the (*) convolution of two functions is equal to the product of the two functions each under this operator. The kernel of this transform is e to the negative s t, making this transform useful for turning differential equations into algebraic equations. For 10 points, name this transform which takes a function from the real time domain to the complex "s" domain, and which is denoted by a capital "L."
If taking this operator on a function f of x yields big f of y, taking this operator on f of a times x yields one over a times big f of quantity y over a according to its "scaling property."
Laplace Transform