1. It is possible to generalize spectral theory to such algebras. 2. Spectral theory also underlies certain aspects of the Fourier transform of a function.3. He is considered one of the founders of the modern Multiparameter Spectral Theory . 4. Unital Banach algebras over the complex field provide a general setting to develop spectral theory . 5. He wrote five papers directly related to spectral theory of operators which Hilbert was developing. 6. There have been three main ways to formulate spectral theory , all of which retain their usefulness. 7. Some applications have required the development of " p "-adic functional analysis and spectral theory . 8. Answering such questions is the realm of spectral theory and requires considerable background in functional analysis and matrix algebra. 9. The role of spectral theory arises in establishing the nature and existence of the basis and the reciprocal basis. 10. The spectral theory of compact operators then follows, and it is due to Frigyes Riesz ( 1918 ).
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