A remark on the Laplace transform
- The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.
| Author details: | W. Chelkh, Ibrahim LyGND, Nikolai TarkhanovORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1134/S0037446620040151 |
| ISSN: | 0037-4466 |
| ISSN: | 1573-9260 |
| Title of parent work (English): | Siberian Mathematical Journal |
| Publisher: | Consultants Bureau, Springer |
| Place of publishing: | New York |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/07/29 |
| Publication year: | 2020 |
| Release date: | 2023/02/06 |
| Tag: | Fourier-Laplace transform; analytic functional; distributions with one-sided support; holomorphic function |
| Volume: | 61 |
| Issue: | 4 |
| Number of pages: | 8 |
| First page: | 755 |
| Last Page: | 762 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
