- #1
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What is the justification for this inequality?
\int_0^1(|u(s)|+|v(s)|)(|u(s)|-|v(s)|)ds\leq \left(\int_0^1(|u(s)|^2+|v(s)|^2)ds\right)^{1/2}\left(\int_0^1(|u(s)-v(s)|^2)ds\right)^{1/2}
where u and v are complex-valued square-integrable Riemann integrable functions on [0,1].
Thx.
\int_0^1(|u(s)|+|v(s)|)(|u(s)|-|v(s)|)ds\leq \left(\int_0^1(|u(s)|^2+|v(s)|^2)ds\right)^{1/2}\left(\int_0^1(|u(s)-v(s)|^2)ds\right)^{1/2}
where u and v are complex-valued square-integrable Riemann integrable functions on [0,1].
Thx.
