Generalized Fourier representation of the absolutely continuous part of a selfadjoint operator
Functional Analysis
2011-03-25 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
We formulate and prove the existence and uniqueness of the generalized Fourier transform associated with the absolutely continuous part of an arbitrary selfadjoint operator on a separable Hilbert space. To this end we develop a novel method to decompose an absolutely continuous operator into a variable fiber direct integral of selfadjoint operators.
Keywords
Cite
@article{arxiv.1103.4682,
title = {Generalized Fourier representation of the absolutely continuous part of a selfadjoint operator},
author = {Take-Yuki Nagao},
journal= {arXiv preprint arXiv:1103.4682},
year = {2011}
}