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A study is made of the eigenvalues of self-adjoint Toeplitz operators on multiply connected planar regions having g holes. The presence of eigenvalues is detected through an analysis of the zeros of translations of theta functions restricted to R g in C g .doi:10.1090/s0002-9939-04-07273-9 fatcat:cbfum76ks5d6xnga4ldvlvsz4y