# Tag Info

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• 4,336
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### Every self-adjoint trace class operator on $L^2$ has integral kernel

Yes, this is correct. Actually, "self-adjoint trace-class" is more than you need; any Hilbert-Schmidt operator can be represented as an integral operator. The Hilbert-Schmidt operators from $L^2(X)$ ...
• 37.4k
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• 1,163

• 78.3k
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### Trace-class properties of integral operator

$k$ being compactly generated, you can as well assume that $k$ is a smooth function defined on $\mathbb{T}^2$ and $Op(k)$ acts on $L^2(\mathbb T)$ (for $\mathbb{T} = \mathbb R/\mathbb Z$ the unit ...
• 8,455
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• 13.2k
1 vote
Accepted

• 13.2k
1 vote
Accepted

### Various limits of the Christoffel Darboux Kernel

It seems that both questions receive some answers in this paper. In th $L^2$ norm, Section 9 seems to stipulate convergence and a limit $K$. For the uniform and pointwise convergence, we have on p. ...
• 3,200
1 vote

### Error estimate in the spectral theorem of compact operators on a Hilbert space

Actually, the presumption that the partial sums of the kernel converge to it in $L^2$ of the product is not quite right: for example, mapping $\ell^2\to \ell^2$ by $e_n\to \lambda_n\cdot e_n$ for a ...
• 21.3k
1 vote
Accepted

### Fredholm integral with functions constrained to [0;1]

There is not enough information for a thorough answer. An a priori bound on the solution may indeed help theoretically and practically. As usual with measured data you may not want to solve the ...
• 11.6k

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