LAUSR

ABSTRACT For two real numbers we study some spectral properties of the weighted finite bilateral Laplace transform operator, defined over the space by In particular, we use a technique based on the Min–Max theorem to prove that the sequence of the eigenvalues of this operator has a super-exponential decay rate to zero. Moreover, we give a lower bound with a magnitude of order for the largest eigenvalue of the operator Also, we give some local estimates and bounds of the eigenfunctions of Moreover, we show that these eigenfunctions are good candidates for the spectral approximation of a function that can be written as a weighted finite Laplace transform of an other function. Finally, we give some numerical examples that illustrate the different results of this work. In particular, we provide an example that illustrate the Laplace-based spectral method, for the inversion of the finite Laplace transform.