Functional calculus via Laplace transform and equations with infinitely many derivatives. (English) Zbl 1314.34135
Summary: We study nonlocal linear equations of the form \(f(\partial_t)\phi = J(t),\; t \geq 0\), in which \(f\) is an entire function. We develop an appropriate functional calculus via Laplace transform, we solve the aforementioned equation completely in the space of exponentially bounded functions, and we analyze the delicate issue of the formulation of initial value problems for nonlocal equations.{
©2010 American Institute of Physics}
©2010 American Institute of Physics}
MSC:
| 34K05 | General theory of functional-differential equations |
| 34K17 | Transformation and reduction of functional-differential equations and systems, normal forms |
| 44A10 | Laplace transform |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83E30 | String and superstring theories in gravitational theory |
| 83F05 | Relativistic cosmology |
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