### Abstract

This entry formalizes the Laplace transform and concrete Laplace transforms for arithmetic functions, frequency shift, integration and (higher) differentiation in the time domain. It proves Lerch's lemma and uniqueness of the Laplace transform for continuous functions. In order to formalize the foundational assumptions, this entry contains a formalization of piecewise continuous functions and functions of exponential order.

### License

BSD License

### Topics

- Mathematics/Analysis

### Session Laplace_Transform

- Laplace_Transform_Library
- Piecewise_Continuous
- Existence
- Lerch_Lemma
- Uniqueness
- Laplace_Transform

## Cite

×

Laplace_Transform-AFP

    @article{Laplace_Transform-AFP,
      author  = {Fabian Immler},
      title   = {Laplace Transform},
      journal = {Archive of Formal Proofs},
      month   = {August},
      year    = {2019},
      note    = {\url{https://isa-afp.org/entries/Laplace_Transform.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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