Titlebook: Spectral Theory of Dynamical Systems; Second Edition Mahendra Nadkarni Book 2020 Hindustan Book Agency 2020 and Springer Nature Singapore P

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Metamorphosis

978-981-15-6227-3Hindustan Book Agency 2020 and Springer Nature Singapore Pte Ltd 2020

Discrete

机密

Texts and Readings in Mathematicshttp://image.papertrans.cn/s/image/873874.jpg

Enervate

健壮

The Hahn-Hellinger Theorem,In this chapter we define spectral measure on a complex separable Hilbert space and state and prove the key theorem due to Hahn and Hellinger which describes such measures concretely and provides a complete invariant for unitary equivalence of two spectral measures.

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Exonerate

Symmetry and Denseness of the Spectrum,In this chapter we prove two properties of the spectrum of the unitary operator associated with an aperiodic non-singular automorphism, viz., that it is symmetric and fills the entire unit circle. We also discuss the spectrum of such an operator multiplied by a unitary function.

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Multiplicity and Rank,The rank of a measure preserving automorphism . is greater than or equal to the spectral multiplicity of .. This is true for a class of non-singular automorphisms as well.

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The Skew Product,In this chapter we will discuss the idea of skew product in its ‘simplest’ form. It is a very useful method, due to Anzai, of constructing new automorphisms from known ones.