The integral equation methods for the perturbed Helmholtz eigenvalue problems.
The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle
This paper provides sufficient conditions on a quasisymmetric automorphism γ of the unit circle which guarantee the existence of the smallest positive eigenvalue of γ. They are expressed by means of a regular quasiconformal Teichmüller self-mapping φ of the unit disc Δ. In particular, the norm of the generalized harmonic conjugation operator is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest positive eigenvalue...
The spectrum of the transport operator with a potential term under the spatial periodicity condition