Quantizations of Linear Self-maps of R
ثبت نشده
چکیده
We investigate the dynamics and spectral properties of the unitary operators Uλ := e iλxF , where λ ∈ R and F is the Fourier transform. We show that Uλ is a quantization of the classical map fλ : R 2 → R (x, y) 7→ (y, 2λy − x), and that the phase transition at |λ| = 1 for fλ corresponds to a similar phase transition for Uλ, which changes at those values from having a pure point to a continuous spectrum.
منابع مشابه
Spectrum Preserving Linear Maps Between Banach Algebras
In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.
متن کاملSpectral Properties and Dynamics of Quantized Henon Maps
We study a generalization of the Airy function, and use its properties to investigate the dynamics and spectral properties of the unitary operators on L2(R) of the form Uc := Fei(q(x)+cx), where q is a real polynomial of odd degree, c a real number, and F the Fourier transform. We show that Uc is a quantization of the classical Henon map fλ : R 2 → R (x, y) 7→ (y + q′(x) + c,−x), and show that ...
متن کاملLinear maps preserving or strongly preserving majorization on matrices
For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...
متن کاملHölder continuity of solution maps to a parametric weak vector equilibrium problem
In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.
متن کاملUnique common coupled fixed point theorem for four maps in $S_b$-metric spaces
In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002