Direct solution of general one-dimensional linear parabolic equation via an abstract plancherel formula.
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.
Hersh
R
R
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF NEW MEXICO, ALBUQUERQUE.