Suppose $f$ and $g$ are Schwartz functions. Does the following result hold?
$\sup_x|f(x)g(x)|=\sup_x|f(x)|\sup_x|g(x)|$
In general, for what class of functions this is valid ? Or is it that this relation is always true ?
Suppose $f$ and $g$ are Schwartz functions. Does the following result hold?
$\sup_x|f(x)g(x)|=\sup_x|f(x)|\sup_x|g(x)|$
In general, for what class of functions this is valid ? Or is it that this relation is always true ?
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