Regularization of the non-stationary Schrödinger operator

2009 ◽  
Vol 32 (5) ◽  
pp. 535-555 ◽  
Author(s):  
Paula Cerejeiras ◽  
Nelson Vieira
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Stationary Schrödinger Operator

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.

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.

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This article has been retracted.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 A THEOREM OF PHRAGMÉN-LINDELÖF TYPE FOR SUBFUNCTIONS IN A CONE

2011 ◽  
Vol 53 (3) ◽  
pp. 599-610 ◽  
Author(s):  
LEI QIAO ◽  
GUANTIE DENG
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Stationary Schrödinger Operator ◽  
Lindelöf Theorem ◽  
Harmonic Majorant

AbstractFor a subfunction u, associated with the stationary Schrödinger operator, which is dominated on the boundary by a certain function on a cone, we generalise the classical Phragmén-Lindelöf theorem by making an a-harmonic majorant of u.

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