Question

2 Prove that if f,ginL^(2)(mu ), then ||f||^(2)||g||^(2)-|(:f,g:)|^(2)=(1)/(2)∬|f(x)g(y)-g(x)f(y)|^(2)dmu (y)dmu (x). 2Prove that if fgE L2,then I|f|2||g|2-|(f,g|2= [lf(x)g(y)-8(x)f(y)|2d(y)d(x)

Name: 2 prove that if fginl2mu then f2g2 fg212fxgy gxfy2dmu ydmu x 2prove that if fge l2then if2g2 fg2 lfxgy 8xfy2dydx 45578
Uploaded: 2022-06-21T21:01:07-08:00
Duration: 5 min 41 s
Channel: Sri K
Description: 2 prove that if fginl2mu then f2g2 fg212fxgy gxfy2dmu ydmu x 2prove that if fge l2then if2g2 fg2 lfxgy 8xfy2dydx 45578

          2 Prove that if f,ginL^(2)(mu ), then
||f||^(2)||g||^(2)-|(:f,g:)|^(2)=(1)/(2)∬|f(x)g(y)-g(x)f(y)|^(2)dmu (y)dmu (x).
2Prove that if fgE L2,then
I|f|2||g|2-|(f,g|2=
[lf(x)g(y)-8(x)f(y)|2d(y)d(x)

Added by Asunci-N T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/21/2022

Step 1

Step 1: Start with the definition of the inner product in L^2 space: ||f||^2 = (:f,f:) Show more…

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2 Prove that if f,ginL^(2)(mu ), then ||f||^(2)||g||^(2)-|(:f,g:)|^(2)=(1)/(2)∬|f(x)g(y)-g(x)f(y)|^(2)dmu (y)dmu (x). 2Prove that if fgE L2,then I|f|2||g|2-|(f,g|2= [lf(x)g(y)-8(x)f(y)|2d(y)d(x)