In the space Cf1,1], we define the inner product (/,> = /_!, - t2f(t)g(t)dt = \ fl 1 Vl
Chapter 5, Problem 34(choose chapter or problem)
In the space Cf1,1], we define the inner product (/,> = /_!, - t2f(t)g(t)dt = \ fl 1 Vl - t2f(t)g(t)dt. See Exercise 33; here we let w(t) = -V l - f2. [This function w(t) is called a Wigner Semicircle Distribution, after the Hungarian physicist and mathematician E. P. Wigner (1902-1995), who won the 1963 Nobel Prize in Physics.] Since this is not a course in calculus, here are some inner products that will turn out to be useful: (l,f2) = 1/4, (f,f3) = 1/8, and
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