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Let $A$ be a self-adjoint operator with domain $D(A)\subset\mathcal H$ ($\mathcal H$ is some Hilbert space). An operator $C$ with $D(A)\subset D(C)$ is called relatively compact with respect to $C$ if ...

Most antiderivative of $g$ are not in $L^1(\mathbb{R})$, in your case only one antiderivative $G_0$ will be in $L^1(\mathbb{R})$, the one actually equal to $f$. All the other antiderivatives $G$ are ...

For the differential equation $ f^{(n)}(x) = c^n x^a f(x) $ with $ c \neq 0 $ a complex number and $ a > 0 $ a real number, the possible behaviors at infinity are known, see Example 5 Section 3.4 ...

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