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  "body": "\n## Definition\n\nLet $T$ be an [[integral transform|YCK709QB06]], defined on a class $A$ of functions.\nA *transform pair* for $T$ is a pair $(f, F)$ with $f \\in A$ and $F = Tf$.\nIt is written $f \\leftrightarrow F$.\n\n## Remarks\n\nExample: for the Laplace transform $T$ and a real number $a$, the pair $(e^{at}, 1/(s - a))$ is a transform pair, because $\\int_0^\\infty e^{at} e^{-st}\\, dt = 1/(s - a)$ for $s \u003e a$.\nNon-example: $(1, 1/s^2)$ is not a Laplace transform pair, because the Laplace transform of $1$ is $1/s$, not $1/s^2$.\nWhen $T$ is injective on $A$, each $F$ in the image determines $f$, and the pair can be read in both directions.\n",
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