Wavelet-based integral representation for solutions of the wave equation

Details Wavelet-based integral representation for solutions of the wave equation Wavelet-based integral representation for solutions of the wave equation

2008-09-12

arxiv.org/abs/0809.2211v1

Physics

Mathematical Physics

29 pages; submitted to J. Phys. A: Math. Theor

Scientific paper

An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on mathematical techniques of continuous wavelet analysis. The formulas obtained are justified from the point of view of distribution theory. A comparison of the results with those by G. Kaiser is carried out. Methods of obtaining physical wavelets are discussed.

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