DIRECT SOLUTION OF GENERAL ONE-DIMENSIONAL LINEAR PARABOLIC EQUATION VIA AN ABSTRACT PLANCHEREL FORMULA

AUTOR(ES)

Hersh, Reuben

RESUMO

We use the formalism of Fourier transformation to derive a functional calculus for the generator of an abstract group. As an application we obtain a new direct solution of Cauchy's problem for one-dimensional stationary parabolic equations of arbitrary order with bounded coefficients.

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