Abstract
We consider the equation (0.1) with f(x)∈D’(ℝn). The solution u(x) of this equation is also sought in D’(ℝn). Let us applying the Fourier transformation to both sides of (0.1). This results, in view of formula (4.8) in Chap. 2, in the “algebraic” equation {Equa 165-1} where the equality is understood as the equality of functionals belonging to Z’(ℂn).
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© 1994 Springer-Verlag Berlin Heidelberg
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Egorov, Y.V., Shubin, M.A. (1994). Existence and Uniqueness of Solutions of Differential Equations. In: Egorov, Y.V., Shubin, M.A. (eds) Partial Differential Equations II. Encyclopaedia of Mathematical Sciences, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57876-2_11
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DOI: https://doi.org/10.1007/978-3-642-57876-2_11
Publisher Name: Springer, Berlin, Heidelberg
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