Linear Peridynamics Fourier Multipliers and Eigenvalues

A characterization for the Fourier multipliers and eigenvalues of linear peridynamic operators is provided. The analysis presented state-based isotropic homogeneous media in any spatial dimension. We provide explicit formulas terms space dimension, nonlocal parameters, material properties. approach we follow based on multiplier developed by Alali Albin (Applicable Analysis 2526–2546, 1). are second-order tensor fields, which given through integral representations. It shown that can be derived directly from tensors. reveal a simple structure hypergeometric functions, allows providing representations as well eigenvalues. These utilized to show convergence peridynamics Navier operator elasticity limit vanishing nonlocality. Moreover, representation compute spectrum operators.