Essential Self-adjointness of the Wave Operator and the Limiting Absorption Principle on Lorentzian Scattering Spaces

نویسندگان

  • ANDRÁS VASY
  • ANDRAS VASY
چکیده

We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show dense range of − λ, λ / ∈ R, in Lsc when acting on an appropriate subdomain.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

m at h . SP ] 2 8 N ov 2 00 8 ABSOLUTELY CONTINUOUS AND SINGULAR SPECTRAL SHIFT FUNCTIONS

Given a self-adjoint operator H0, a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure Λ(H0, F) ⊂ R is defined, such that for all points of this set the wave and the scattering matrices can be defined unambiguously. Many well-known properties of the wave and sc...

متن کامل

ar X iv : 0 81 0 . 20 72 v 1 [ m at h . SP ] 1 2 O ct 2 00 8 ABSOLUTELY CONTINUOUS AND SINGULAR SPECTRAL SHIFT FUNCTIONS

Given a self-adjoint operator H 0 , a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure Λ(H 0 , F) ⊂ R is defined, such that for all points of this set the wave and the scattering matrices can be defined unambiguously. Many well-known properties of the wave an...

متن کامل

Discretized Laplacians on an Interval and Their Renormalization Group

The Laplace operator admits infinite self-adjoint extensions when considered on a segment of the real line. They have different domains of essential self-adjointness characterized by a suitable set of boundary conditions on the wave functions. In this paper we show how to recover these extensions by studying the continuum limit of certain discretized versions of the Laplace operator on a lattic...

متن کامل

Nonlinear Responses and Optical Limiting Behavior of Ag Nanoparticle Suspension

In this study, the nonlinear optical properties and optical limiting performance of the silver nanoparticles (AgNPs) in distilled water are investigated. The nonlinear absorption coefficient of the colloid is measured by the Z-scan technique. The optical limiting behavior of the AgNP suspension is investigated under exposure to nanosecond laser pulses at 532 nm. The results show that nonlinear ...

متن کامل

Essential Self–adjointness and Global Hypoellipticity of the Twisted Laplacian

A scale of Sobolev spaces is introduced to measure the global hypoellipticity of the twisted Laplacian. The essential self-adjointness of the twisted Laplacian is established and the domain of the unique self-adjoint extension is determined in terms of the Sobolev spaces. The global hypoellipticity of the twisted Laplacian in the Gelfand–Shilov spaces is also proved. 1. The twisted Laplacian Le...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017