  With its third data release, European Space Agency's Gaia mission publishes
for the first time low resolution spectra for a large number of celestial
objects. These spectra however differ in their nature from typical
spectroscopic data. They do not consist of wavelength samples with associated
flux values, but are represented by a linear combination of Hermite functions.
We derive an approach to the study of spectral lines that is robust and
efficient for spectra that are represented as a linear combination of Hermite
functions. For this purpose, we combine established computational methods for
orthogonal polynomials with the peculiar mathematical properties of Hermite
functions and basic properties of the Gaia spectrophotometers. Particular use
is made of the simple computation of derivatives of linear combinations of
Hermite functions and their roots. A simple and efficient computational method
for deriving the position in wavelength, the statistical significance, and the
line strengths is presented for spectra represented by a linear combination of
Hermite functions. The derived method is fast and robust enough to be applied
to large numbers of Gaia spectra without high performance computing resources
or human interaction. Example applications to hydrogen Balmer lines, He I
lines, and a broad interstellar band in Gaia DR3 low resolution spectra are
presented.

Instrumentation and Methods for Astrophysics;Solar and Stellar Astrophysics