Perturbation of a self adjoint differential operator

An Unusual Self-adjoint Linear Partial Differential Operator

In an American Mathematical Society Memoir, to appear in 2003, the authors Everitt and Markus apply their prior theory of symplectic algebra to the study of symmetric linear partial differential expressions, and the generation of self-adjoint differential operators in Sobolev Hilbert spaces. In the case when the differential expression has smooth coefficients on the closure of a bounded open re...

Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at ±∞. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of ...

Perturbation of multiparameter non-self-adjoint boundary eigenvalue problems for operator matrices

We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter λ and on the vector of real physical parameters p. We study perturbations of semi-simple multiple eigenvalues as well as pertu...

The Laplace operator is essentially self-adjoint

High order fitted operator numerical method for self-adjoint singular perturbation problems

We consider self-adjoint singularly perturbed two-point boundary value problems in conservation form. Highest possible order of uniform convergence for such problems achieved hitherto, via fitted operator methods, was one (see, e.g., [Doolan et al. Uniform numerical methods for problems with initial and boundary layers, Boole Press, Dublin, 1980], p. 121]). Reducing the original problem into th...