scholarly journals Criteria of Wiener Type for Minimally Thin Sets and Rarefied Sets Associated with the Stationary Schrödinger Operator in a Cone

2012 ◽  
Vol 2012 ◽  
pp. 1-29
Author(s):  
Pinhong Long ◽  
Zhiqiang Gao ◽  
Guantie Deng
Keyword(s):  
Schrödinger Operator ◽  
Boundary Point ◽  
Martin Boundary ◽  
Schrodinger Operator ◽  
Stationary Schrödinger Operator ◽  
Thin Set ◽  
Thin Sets ◽  
Wiener Type ◽  
Minimally Thin Set ◽  
Rarefied Set

We give some criteria fora-minimally thin sets anda-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or ∞ with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside ana-rarefied set. Finally we illustrate the relation between thea-minimally thin set and thea-rarefied set in a cone.

scholarly journals Retraction Note: Minimally thin sets associated with the stationary Schrödinger operator

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tao Zhao
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Link Type ◽  
Stationary Schrödinger Operator ◽  
Thin Sets ◽  
Retraction Notice

This article has been retracted. Please see the Retraction Notice for more detail: 10.1186/s13660-021-02575-1

scholarly journals On the relationship between ordinary thin sets and full-thin sets

1980 ◽  
Vol 29 (3) ◽  
pp. 348-361
Author(s):  
J. S. Hwang ◽  
H. L. Jackson
Keyword(s):  
Unit Ball ◽  
Half Space ◽  
Boundary Point ◽  
Subject Classification ◽  
Thin Set ◽  
Thin Sets ◽  
The Relationship

AbstractIn this work we demonstrate that if Ω ⊂ Rn (n ≧ 3) is either a half space or a unit ball, and if E ⊂ ω then E is an ordinary thin set at a boundary point of Ω (including the point at infinity if Ω is a half space) if and only if it is a full-thin set at the corresponding Kuramochi boundary point of Ω. The case for n = 2 has already been considered in an earlier work.1980 Mathematics subject classification (Amer. Math. Soc.): 31 B 05.

Beurling-Dahlberg-Sjögren Type Theorems for Minimally Thin Sets in a Cone

2003 ◽  
Vol 46 (2) ◽  
pp. 252-264 ◽  
Author(s):  
Ikuko Miyamoto ◽  
Minoru Yanagishita ◽  
Hidenobu Yoshida
Keyword(s):  
Half Space ◽  
Corner Point ◽  
Smooth Boundary ◽  
Thin Set ◽  
Special Domain ◽  
Thin Sets ◽  
Minimally Thin Set

AbstractThis paper shows that some characterizations of minimally thin sets connected with a domain having smooth boundary and a half-space in particular also hold for the minimally thin sets at a corner point of a special domain with corners, i.e., the minimally thin set at ∞ of a cone.

GENERALIZATION OF THE PHRAGMÉN–LINDELÖF THEOREMS FOR SUBFUNCTIONS

2013 ◽  
Vol 24 (08) ◽  
pp. 1350062 ◽  
Author(s):  
LEI QIAO ◽  
GUOSHUANG PAN
Keyword(s):  
Schrödinger Operator ◽  
Integral Representations ◽  
Schrodinger Operator ◽  
Stationary Schrödinger Operator ◽  
Lindelöf Theorem ◽  
Harmonic Majorants

In this paper, we consider the Phragmén–Lindelöf theorem for subfunctions, associated with the stationary Schrödinger operator. Meanwhile, the integral representations and a-harmonic majorants of them are also given.

Sign in / Sign up

Export Citation Format

Share Document