Laplace transform methods in multivariate spectral theory

Laplace Transform, Dynamics and Spectral Geometry

We consider vector fields X on a closed manifold M with rest points of Morse type. For such vector fields we define the property of exponential growth. A cohomology class ξ ∈ H(M ;R) which is Lyapunov for X defines counting functions for isolated instantons and closed trajectories. If X has exponential growth property we show, under a mild hypothesis generically satisfied, that these counting f...

Dynamics, Laplace Transform and Spectral Geometry∗

We consider a vector field X on a closed manifold which admits a Lyapunov one form. We assume X has Morse type zeros, satisfies the Morse– Smale transversality condition and has non-degenerate closed trajectories only. For a closed one form η, considered as flat connection on the trivial line bundle, the differential of the Morse complex formally associated to X and η is given by infinite serie...

The Laplace transform in control theory

The Laplace transform plays a important role in control theory. It appears in the description of linear time invariant systems, where it changes convolution operators into multiplication operators and allows to define the transfer function of a system. The properties of systems can be then translated into properties of the transfer function. In particular, causality implies that the transfer fu...

Numerical Methods for Laplace Transform Inversion

Laplace Transform Methods for Evolution Equations

The Laplace transform theory of Banach space valued functions and the field of evolution equations presently offer many research problems which are of general interest in mathematical analysis. Although there is a longstanding relationship between the two fields, it was not until recently that the basic transform principles for Banach space valued functions could be formulated in a satisfactory...