Expansions on generalized eigenvectors of operators arising in the theory of elasticity
Giuseppe Geymonat, Pierre Grisvard · Differential and Integral Equations · 1991
An old problem is revisited: To expand the solutions of an operational differential equation u 1 (t) + Au(t) = 0, t > 0, into sums of exponential-polynomial solutions when A is an unbounded and non-normal operator in a Hilbert space.The assumptions on A are motivated by some examples in the theory of plane elasticity where one wishes to separate variables in polar coordinates.One of the basic tools is the behavior of the Fredholm determinant of A which can be calculated in the examples.