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.

翻译：本文中，频域声场被视为某带限函数空间的元素，并提出将该声场表示为该空间中再生核的线性组合。当仅已知任意位置处的声压信息时，该模型在所有函数系统中具有最强的表示能力。所提模型可视为现有三维声场模型向空间维度的推广，该模型利用亥姆霍兹方程解空间的再生核。以此方式捕捉频域声场的优势之一在于波数谱估计公式的简洁性。通过两组数值模拟验证了所提方法的有效性。