Absolute Continuity and Singularity of Spectra for the Flows \(T_t\otimes T_{at}\)

IF 0.6 4区 数学 Q3 MATHEMATICS
V. V. Ryzhikov
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引用次数: 0

Abstract

Given disjoint countable dense subsets \(C\) and \(D\) of the half-line \((1,+\infty)\), there exists a flow \(T_t\) preserving a sigma-finite measure and such that all automorphisms \(T_1\otimes T_{c}\) with \(c\in C\) have simple singular spectrum and all automorphisms \(T_1\otimes T_{d}\) with \(d\in D\) have Lebesgue spectrum of countable multiplicity.

流动光谱的绝对连续性和奇异性 \(T_t\otimes T_{at}\)
给定半线\((1,+\infty)\)的不相交可数稠密子集\(C\)和\(D\),存在一个流\(T_t\)保持一个σ -有限的量,使得所有与\(c\in C\)的自同构\(T_1\otimes T_{c}\)都具有简单奇异谱,所有与\(d\in D\)的自同构\(T_1\otimes T_{d}\)都具有可数复数的勒贝格谱。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
7
审稿时长
>12 weeks
期刊介绍: Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
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