A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type. (English) Zbl 1079.35527

Summary: The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.


35L10 Second-order hyperbolic equations
42C15 General harmonic expansions, frames
47A60 Functional calculus for linear operators
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