@article{ChelkhLyTarkhanov2020,
  author    = {Chelkh, W. and Ly, Ibrahim and Tarkhanov, Nikolai},
  title     = {A remark on the Laplace transform},
  series = {Siberian Mathematical Journal},
  volume    = {61},
  journal   = {Siberian Mathematical Journal},
  number    = {4},
  publisher = {Consultants Bureau, Springer},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446620040151},
  pages     = {755 -- 762},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}