Spectral Synthesis for Operators and Systems

[摘要] Spectral synthesis is the reconstruction of the whole latticeof invariant subspaces of a linear operator from generalisedeigenvectors. A closely related problem is the reconstructionof a vector in a Hilbert space from its Fourier series with respect to some complete and minimal system. This article discusses the spectral synthesis problem in the context of operator and function theory and presents several recent advancesin this area. Among them is the solution of the spectral synthesis problem for systems of exponentials in L2(−π, π).A more detailed account of these problems can be foundin the survey [1], to appear in the proceedings of 7ECM.