Upper bounds on the number of eigenvalues of stationary Schrödinger operators

2010 ◽  
Vol 51 (8) ◽  
pp. 083523 ◽  
Author(s):  
Dai Shi
Keyword(s):  
Schrödinger Operators ◽  
Upper Bounds ◽  
Schrodinger Operators

Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions

1998 ◽  
Vol 50 (3) ◽  
pp. 538-546 ◽  
Author(s):  
Richard Froese
Keyword(s):  
Simple Proof ◽  
Schrödinger Operator ◽  
Upper Bound ◽  
Counting Function ◽  
Schrödinger Operators ◽  
Upper Bounds ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Odd Dimensions

AbstractThe purpose of this note is to provide a simple proof of the sharp polynomial upper bound for the resonance counting function of a Schrödinger operator in odd dimensions. At the same time we generalize the result to the class of superexponentially decreasing potentials.

Correction to: Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions

2001 ◽  
Vol 53 (4) ◽  
pp. 756-757 ◽  
Author(s):  
Richard Froese
Keyword(s):  
Fourier Transform ◽  
Counting Function ◽  
Schrödinger Operators ◽  
Singular Values ◽  
Upper Bounds ◽  
Schrodinger Operators ◽  
The Fourier Transform ◽  
Odd Dimensions

AbstractThe proof of Lemma 3.4 in [F] relies on the incorrect equality μj(AB) = μj(BA) for singular values (for a counterexample, see [S, p. 4]). Thus, Theorem 3.1 as stated has not been proven. However, with minor changes, we can obtain a bound for the counting function in terms of the growth of the Fourier transform of |V|.

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