Eigenfunction of an integral operator

Summary

An eigenfunction of an integral operator $T_K$ is a nonzero function $\varphi$ with $T_K \varphi = \mu \varphi$ for some number $\mu$. It is an eigenvector of $T_K$ in a space of functions. For symmetric kernels the eigenfunctions can be chosen to form an orthonormal system, and expanding in them diagonalizes the operator, as in the Hilbert–Schmidt theorem.