Let L^2(R)={f:R->C| \int_{\infty}^{\infty} \abs(f(t))^2 < \infty } and L^1(R)={f:R->C| \int_{\infty}^{\infty} \abs(f(t)) < \infty }. Give and example of a function such that f \in L^2(R) and f \notin L^1(R).
Give and example of a function such that f \in L^2(R) and f \notin L^1(R)
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real-analysis
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0@Ross Millikan: I agree, it is a very natural question indeed. – 2010-10-25
1 Answers
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Try to look at a function of the form $f(x) = x^{-a}$ for some a > 0 on an appropriate domain.
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1In this case, you can also look at the list of the questions by the same editor. There has been someone asking homework questions about functional analysis for a few days. – 2010-10-24