Ruelle operators : functions which are harmonic with respect to a transfer operator / Palle E.T. Jorgensen.

Format:

Book

Author/Creator:

Jørgensen, Palle E. T., 1947- author.

Series:

Memoirs of the American Mathematical Society ; no. 720.

Memoirs of the American Mathematical Society, 0065-9266 ; number 720

Language:

English

Subjects (All):

Ruelle operators.

Wavelets (Mathematics).

Physical Description:

1 online resource (74 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2001]

Language Note:

English

Summary:

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

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. A discrete ax + b group""; ""Chapter 3. Proof of Theorem 2.4""; ""Chapter 4. Wavelet filters""; ""Chapter 5. Cocycle equivalence of filter functions""; ""Chapter 6. The transfer operator of Keane""; ""Chapter 7. A representation theorem for R-harmonic functions""; ""Chapter 8. Signed solutions to R(f) = f""; ""Bibliography""

Notes:

"Volume 152 Number 720 (first of 5 numbers)."

Includes bibliographical references (pages 58-60).

Description based on print version record.

ISBN:

1-4704-0313-7