The Trace Formula for Schrödinger Operators from Infinite Dimensional Oscillatory Integrals

1996 ◽  
Vol 182 (1) ◽  
pp. 21-65 ◽  
Author(s):  
Sergio Albeverio ◽  
Anne Boutet De Monvel-Berthier ◽  
Zdzislaw Brzeźniak
Keyword(s):  
Trace Formula ◽  
Schrödinger Operators ◽  
Oscillatory Integrals ◽  
Schrodinger Operators ◽  
Infinite Dimensional

scholarly journals A Trace Formula for Multidimensional Schrödinger Operators

1996 ◽  
Vol 141 (2) ◽  
pp. 449-465 ◽  
Author(s):  
F Gesztesy ◽  
H Holden ◽  
B Simon ◽  
Z Zhao
Keyword(s):  
Trace Formula ◽  
Schrödinger Operators ◽  
Schrodinger Operators

scholarly journals HIGHER ORDER TRACE RELATIONS FOR SCHRÖDINGER OPERATORS

1995 ◽  
Vol 07 (06) ◽  
pp. 893-922 ◽  
Author(s):  
F. GESZTESY ◽  
H. HOLDEN ◽  
B. SIMON ◽  
Z. ZHAO
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Trace Formula ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Trace Formulae ◽  
Derivatives Of

We extend the trace formula recently proven for general one-dimensional Schrödinger operators which obtains the potential V(x) from a function ξ(x, λ) by deriving trace relations computing moments of ξ(λ, x) dλ in terms of polynomials in the derivatives of V at x. We describe the relation of those polynomials to KdV invariants. We also discuss trace formulae for analogs of ξ associated with boundary conditions other than the Dirichlet boundary condition underlying ξ.

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