Titlebook: Spectral Theory of Dynamical Systems; M. G. Nadkarni Book 1998 Hindustan Book Agency 1998

Hangar

Hdl348

Eigenvalues of Non-Singular Automorphisms,nvalue of . if there is a non-zero function .. ∈ ..(., ., .) such that ..(.) = .(.) a.e. .. We call any such .. an .. eigenfunction of . corresponding to the eigenvalue .. Since ||.. ∘ .||. = ||..||. we have |.| = 1. The collection .(.) of .. eigenvalues of . forms a subgroup of the circle group. Fu

有节制

OTHER

Dual Systems of Imprimitivity,he two together yield considerable spectral information. First we recall the definition of a compact group rotation: Let . ⊆ . be a countable infinite group. Let . be the compact dual of ., where . is the group . with the discrete topology. Let . ∈ . be the element defined by .(.) = . for all . ∈ ..

两栖动物

micronutrients

马笼头

Saturated Subgroups of the Circle Group,sures of characters in the respective spaces. We will answer this question in this chapter and discuss its relation to subgroups of the circle group such as the eigenvalue group or the group of quasi-invariance of a measure. As we saw in the previous chapters, such subgroups occur naturally in non-singular dynamics.

领先

A Theorem of Helson and Parry, and +1. The purpose of this chapter is to prove a version of this theorem for hyperfinite actions of countable groups. The improved version is obtained by combining the method of Helson and Parry with the notion of orbit equivalence.

歌曲

Eigenvalues of Non-Singular Automorphisms, to the eigenvalue .. Since ||.. ∘ .||. = ||..||. we have |.| = 1. The collection .(.) of .. eigenvalues of . forms a subgroup of the circle group. Further.Since . is ergodic |..| is constant a.e. .. The function . is an eigenfunction of absolute value one, with eigenvalue .

Lymphocyte

Dual Systems of Imprimitivity, group. Let . be the compact dual of ., where . is the group . with the discrete topology. Let . ∈ . be the element defined by .(.) = . for all . ∈ .. Let . : . → . be defined by . = . + ., . ∈ .. Then the system (., .) is called a compact group rotation.