Seeking for Functional Analysis problems solution

Bando93
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Hello everybody here,

I'm taking Functional Analysis this term, and the textbook is : "An Introduction to Hilbert Space, Cambridge, 1988" by N. Young.

Unfortunately, we have to solve most of the book's problems. So, does anyone has some of them ?

I found a list of solved problems on this link :

http://www.caam.rice.edu/~caam540/index.html

but I can't get the solutions, may be the prof. deleted them

any help will be greatly appreciated.

Cheers
 
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I have that book and it's generally quite a good book. How about trying to solve them for yourself and see how far that gets you.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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