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Justification of a Wavelet-Based Integral Formula for Solutions of the Wave Equation

  • E. A. GorodnitskiyEmail author
  • M. V. Perel
Article

An integral representation of solutions of the wave equation obtained earlier is studied. The integrand contains weighted localized solutions of the wave equation that depend on parameters, which are variables of integration. Dependent on parameters, a family of localized solutions is constructed from one solution by means of transformations of shift, scaling, and the Lorentz transform. Sufficient conditions are derived, which ensure the pointwise convergence of the obtained improper integral in the space of parameters. The convergence of this integral in ℒ2 norm is proved as well. Bibliography: 22 titles.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

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