Abstract Eigenvalue Problem for Monotone Operators and Applications to Differential Operators

In this work we extend the multiple orthogonal sequence method, developed in [3], to the energetic space of an abstract linear monotone operator. This method leads to an abstract eingenvalue problem that it produces orthonormal bases in some nested Hilbert spaces, that they are suitable to develop abstract Fourier or projection methods. Some examples to diceerential operators are also given.