On spectral theory for nonlinear operators
نویسندگان
چکیده
منابع مشابه
A New Spectral Theory for Nonlinear Operators and Its Applications
In this paper, by applying (p, k)-epi mapping theory, we introduce a new definition of spectrum for nonlinear operators which contains all eigenvalues, as in the linear case. Properties of this spectrum are given and comparison is made with the other definitions of spectra. We also give applications of the new theory.
متن کاملLocal Spectral Theory for Operators on BanachSpaces
In this article, we shall discuss some recent developments and applications of the local spectral theory for linear operators on Banach spaces. Special emphasis will be given to those parts of operator theory, where spectral theory, harmonic analysis, and the theory of Banach algebras overlap and interact. Along this line, we shall present the recent progress of the theory of quotients and rest...
متن کاملOn Spectral Theory of Quantum Vertex Operators
In this note we prove a conjecture from [DFJMN] on the asymptotics of the composition of n quantum vertex operators for the quantum affine algebra Uq(ŝl2), as n goes to ∞. For this purpose we define and study the leading eigenvalue and eigenvector of the product of two components of the quantum vertex operator. This eigenvector and the corresponding eigenvalue were recently computed by M.Jimbo....
متن کاملSpectral Theory for Compact Self-Adjoint Operators
This agrees with the definition of the spectrum in the matrix case, where the resolvent set comprises all complex numbers that are not eigenvalues. In terms of its spectrum, we will see that a compact operator behaves like a matrix, in the sense that its spectrum is the union of all of its eigenvalues and 0. We begin with the eigenspaces of a compact operator. We start with two lemmas that we w...
متن کاملSymplectic inverse spectral theory for pseudodifferential operators
We prove, under some generic assumptions, that the semiclassical spectrum modulo O(~) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal symbol.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1977
ISSN: 0022-1236
DOI: 10.1016/0022-1236(77)90050-7