Clark measures on the complex sphere
نویسندگان
چکیده
منابع مشابه
Lens Lectures on Aleksandrov-clark Measures
In this series of three 90 minute lectures I will give a gentle introduction to the topic of Aleksandrov-Clark measures which turn out to have an uncanny way of appearing in various areas of analysis. In short, for an analytic map φ : D→ D, where D is the open unit disk, there is a family {μα : |α| = 1} of positive finite measures on the unit circle T associated with φ by the formula 1− |φ(z)|2...
متن کاملPosition Uncertainty Measures on the Sphere
Position uncertainty (delocalization) measures for a particle on the sphere are proposed and illustrated on several examples of states. The new measures are constructed using suitably the standard multiplication angle operator variances. They are shown to depend solely on the state of the particle and to obey uncertainty relations of the Schrödinger-Robertson type. A set of Hermitian operators ...
متن کاملNull-series on the complex sphere
We construct pluriharmonic null-series on the unit sphere of Cd, d ≥ 2. Also, we give examples when the corresponding spherical harmonics are sparsely distributed and have sufficiently small L2-norms.
متن کاملComplex Analytic Dynamics on the Riemann Sphere
1. Background and notation 2. The dynamical dichotomy of Fatou and Julia 3. Periodic points 4. The consequences of Montel's Theorem 5. The Julia set is the closure of the set of repelling periodic points 6. Classical results concerning the Fatou set 7. Sullivan's classification of the Fatou set 8. A condition for expansion on the Julia set 9. The dynamics of polynomials 10. The Mandelbrot set a...
متن کاملThe Linear Fractional Model Theorem and Aleksandrov-Clark measures
A remarkable result by Denjoy and Wolff states that every analytic self-map φ of the open unit disc D of the complex plane, except an elliptic automorphism, has an attractive fixed point to which the sequence of iterates {φn}n 1 converges uniformly on compact sets: if there is no fixed point in D, then there is a unique boundary fixed point that does the job, called the Denjoy– Wolff point. Thi...
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: 2020
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2019.108314