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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

4 votes
1 answer
127 views

Closure of polynomials in $L^2_w$ with log-normal weight function

Consider the Hilbert space $L^2_w$ with scalar product $\langle f,g\rangle_w =\int_0^\infty f(x)g(x)w(x)dx$ where the weight $w$ is the density function of a log-normal distribution $$ w(x)=\frac{1}{\ …