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On Fourier series in eigenfunctions of elliptic boundary value problems. (English) Zbl 1050.35054

The authors consider an elliptic \(bvp\) of order \(2m\) of the form \[ A(x,D)u(x)=f(x)\in \Omega \]
\[ B_j(x,D)u(x)=0\text{ on }\partial \Omega,\;j=1,\dots,m. \] The coefficients of \(A\) and \(B\) are assumed to be smooth in \(\overline\Omega\) and \(\partial\Omega\). The authors discuss convergence of eigenfunctions in \(H^t(\Omega)\).

MSC:

35P05 General topics in linear spectral theory for PDEs
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
42C15 General harmonic expansions, frames
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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