  We study the spectral dimensions and spectral asymptotics of Krein-Feller
operators for arbitrary finite Borel measures on $\left(0,1\right).$
Connections between the spectral dimension, the $L^{q}$-spectrum, the partition
entropy and the optimised coarse multifractal dimension are established. In
particular, we show that the upper spectral dimension always corresponds to the
fixed point of the $L^{q}$-spectrum of the corresponding measure. Natural
bounds reveal intrinsic connections to the Minkowski dimension of the support
of the associated Borel measure. Further, we give a sufficient condition on the
$L^{q}$-spectrum to guarantee the existence of the spectral dimension. As an
application, we confirm the existence of the spectral dimension of
self-conformal measures with or without overlap as well as of certain measures
of pure point type. We construct a simple example for which the spectral
dimension does not exist and determine explicitly its upper and lower spectral
dimension.
