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Results tagged with fa.functional-analysis
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user 133709
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
0
answers
94
views
system of Laguerre polynomials is orthonormal basis in space $L_2((0, \infty),e^{-t}dt)$ [closed]
Can you help me to prove that system of Laguerre polynomials
$$ L_n = \dfrac{e^t}{n!}\dfrac{d^n}{dt^n} (t^n e^{-t})$$ is orthonormal basis in space $L_2((0, \infty),e^{-t}dt)$ ?
- 21
-1
votes
1
answer
127
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Prove that Cartesian composition $c_0 \times c_0$ is not isometric isomorphic [closed]
Prove that Cartesian composition $c_0 \times c_0$ with rate $ \Vert (x_1 ,x_2)\Vert = \Vert x_1 \Vert_{c_0} + \Vert x_2 \Vert_{c_0} $ is not isometric isomorphic to space $c_0$.
- 21