# The initial value problem for ordinary differential equations with infinitely many derivatives

@article{Grka2012TheIV, title={The initial value problem for ordinary differential equations with infinitely many derivatives}, author={Przemyslaw G{\'o}rka and Humberto Prado and Enrique G. Reyes}, journal={Classical and Quantum Gravity}, year={2012}, volume={29} }

We study existence, uniqueness and regularity of solutions for ordinary differential equations with infinitely many derivatives such as (linearized versions of) nonlocal field equations of motion appearing in particle physics, nonlocal cosmology and string theory. We develop a Lorentzian functional calculus via Laplace transform which allows us to interpret rigorously operators of the form f(∂t) on the half line, in which f is an analytic function. We find the most general solution to the…

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