scholarly journals Decoupling of deficiency indices and applications to Schrödinger-type operators with possibly strongly singular potentials

2016 ◽  
Vol 301 ◽  
pp. 1022-1061 ◽  
Author(s):  
Fritz Gesztesy ◽  
Marius Mitrea ◽  
Irina Nenciu ◽  
Gerald Teschl
Keyword(s):  
Singular Potentials ◽  
Deficiency Indices ◽  
Schrödinger Type Operators ◽  
Strongly Singular Potentials

Minimal Operators for Schrodinger-Type Differential Expressions with Discontinuous Principal Coefficients

1980 ◽  
Vol 32 (6) ◽  
pp. 1423-1437 ◽  
Author(s):  
M. Faierman ◽  
I. Knowles
Keyword(s):  
Basic Problem ◽  
Adjoint Operator ◽  
General Setting ◽  
Equivalence Classes ◽  
The Self ◽  
Singular Potentials ◽  
Image Position ◽  
Schrödinger Type Operators ◽  
Complex Valued

The objective of this paper is to extend the recent results [7, 8, 9] concerning the self-adjointness of Schrödinger-type operators with singular potentials to a more general setting. We shall be concerned here with formally symmetric elliptic differential expressions of the form1.1where x = (x1, …, xm) ∈ Rm (and m ≧ 1), i = (–1)1/2, ∂j = ∂/∂xj, and the coefficients ajk, bj and q are real-valued and measurable on Rm.The basic problem that we consider is that of deciding whether or not the formal operator defined by (1.1) determines a unique self-adjoint operator in the space L2(Rm) of (equivalence classes of) square integrable complex-valued functions on Rm.

scholarly journals Commutation methods for Schrödinger operators with strongly singular potentials

2011 ◽  
Vol 285 (4) ◽  
pp. 392-410 ◽  
Author(s):  
Aleksey Kostenko ◽  
Alexander Sakhnovich ◽  
Gerald Teschl
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Singular Potentials ◽  
Strongly Singular Potentials
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