MIT18_024S11_Pset1

# MIT18_024S11_Pset1 - f pointwise Prove both of these facts...

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PSET 1 - DUE FEBRUARY 8 1. 1.10:22 (6 points) 2. 1.13:11a,b,d (6 points) 3. 2.4:29 (12 points) 4. Last semester we considered pointwise and uniform convergence of functions. Now we consider a diﬀerent type of convergence. Let { f j } be a sequence of functions in L 2 ( R ). We say f j f strongly in L 2 if there exists f L 2 ( R ) such that || f j f || L 2 ( R ) 0 . Give an example of a sequence { f j } and a function f such that f j f strongly in L 2 but f j does not converge to

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Unformatted text preview: f pointwise. Prove both of these facts about your example. (6 points) 1 MIT OpenCourseWare http://ocw.mit.edu 18.024 Multivariable Calculus with Theory Spring 2011 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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MIT18_024S11_Pset1 - f pointwise Prove both of these facts...

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