  In this paper, the frequency-domain sound field is regarded as an element of
some band-limited function space, and a representation of the field as a linear
combination of the reproducing kernel in that space is proposed. This model has
the strongest representational capacity of all function systems when we know
only the sound pressure information at arbitrary positions. The proposed model
can be considered a generalization of the existing three-dimensional sound
field model using the reproducing kernel of the solution space of the Helmholtz
equation to the spatial dimension. One of the advantages of capturing the
frequency-domain sound field in this way is the simplicity achieved for the
estimation formula of the wavenumber spectrum. Two numerical simulations were
conducted to validate the proposed methods.
