multiplicative number theory

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21: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►If an eigenvalue has multiplicity $>1$, the eigenfunctions may always be orthogonalized in this degenerate sub-space. … ► … ►, of unit multiplicity, unless otherwise stated. … ►Letting $n$ run from $-\mathrm{\infty }$ to $\mathrm{\infty }$ this multiplicity change is automatically included: … ►If an eigenvalue is of multiplicity greater than $1$ then an orthonormal basis of eigenfunctions can be given for the eigenspace. …