Abstract
Hypersingular operators play a key role in the mathematical modeling of non-local interactions, particularly in the field of peridynamics, where they provide a powerful tool for understanding material behavior under stress. This paper investigates the spectral characteristics of hypersingular operators and their impact on the solutions of peridynamic equations. Special attention is given to the spectral decomposition of these operators to gain insights into their stability, convergence, and computational efficiency in solving complex problems related to fracture mechanics and material deformation.
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