Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel, e-mail evg@techunix.technion.ac.il
Abstract: 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.
Keywords: elliptic operators, eigenfunctions, Fourier series, hyperbolic equation
Classification (MSC 2000): 35L10, 42C15, 47A60
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