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Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator

其他書名	Functions which are Harmonic with Respect to a Transfer Operator
出版	American Mathematical Soc., 2001
主題	Mathematics / Algebra / LinearMathematics / CalculusMathematics / Mathematical AnalysisMathematics / Functional Analysis
ISBN	08218268839780821826881
URL	http://books.google.com.hk/books?id=JpTUCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋Let $N\in\mathbb{N}$, $N\geq2$, be given. Motivated by wavelet analysis, this title considers a class of normal representations of the $C DEGREES{\ast}$-algebra $\mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU DEGREES{-1}=V DEGREES{N}$. The representations are in one-to-one correspondence with solutions $h\in L DEGREES{1}\left(\mathbb{T}\right)$, $h\geq0$, to $R\left(h\right)=h$ where $R$ is a certain transfer operator (positivity-preserving) which was studied previously by D. Ruelle. The representations of $\mathfrak{A}_{N}$ may also be viewed as representations of a certain (discrete) $N$-adic $ax+b$ group which was considered recently