Eigenvalue Expansion of Nonsymmetric Linear Compact Operators in Hilbert Space

For a symmetric linear compact resp. densely defined operator with inverse, expansion theorems in series of eigenvectors are known. The aim the present paper is to generalize known case corresponding operators without symmetry property. this, we replace set orthonormal by biorthonormal principal vectors simple eigenvalues general eigenvalues. results for property all new. Furthermore, if symmetric, generalized deliver expansions. As an application nonsymmetric eigenvalues, obtain eigenfunctions non-selfadjoint Boundary Eigenvalue Problem ordinary differential discussed book Coddington/Levinson. But, new result general, that is, not necessarily simple. In addition, 2nd order constant coefficients, and Green’s function explicitly determined. This also new, as far author aware.