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This chapter is devoted to spectral measures and (the multiplication form of) the spectral theorem being powerful tools to study unitary and self-adjoint operators on Hilbert spaces via Fourier analysis. We also discuss some decomposition results connecting measure theory and unitary operators, as well as Rajchman and Lebesgue spectrum properties.

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The Spectral Theorem

  • 章节

  • 发表日期：

    2025年

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  • Tanja Eisner,
  • Bálint Farkas

摘要

This chapter is devoted to spectral measures and (the multiplication form of) the spectral theorem being powerful tools to study unitary and self-adjoint operators on Hilbert spaces via Fourier analysis. We also discuss some decomposition results connecting measure theory and unitary operators, as well as Rajchman and Lebesgue spectrum properties.