  A passive approximation problem is formulated where the target function is an
arbitrary complex valued continuous function defined on an approximation domain
consisting of a finite union of closed and bounded intervals on the real axis.
The norm used is a weighted $\text{L}^p$-norm where $1\leq p\leq\infty$. The
approximating functions are Herglotz functions generated by a measure with
H\"{o}lder continuous density in an arbitrary neighborhood of the approximation
domain. Hence, the imaginary and the real parts of the approximating functions
are H\"{o}lder continuous functions given by the density of the measure and its
Hilbert transform, respectively. In practice, it is useful to employ finite
B-spline expansions to represent the generating measure. The corresponding
approximation problem can then be posed as a finite-dimensional convex
optimization problem which is amenable for numerical solution. A constructive
proof is given here showing that the convex cone of approximating functions
generated by finite uniform B-spline expansions of fixed arbitrary order
(linear, quadratic, cubic, etc) is dense in the convex cone of Herglotz
functions which are locally H\"{o}lder continuous in a neighborhood of the
approximation domain, as mentioned above. As an illustration, a typical
physical application example is included regarding the passive approximation
and optimization of a linear system having metamaterial characteristics.
