THE ANALYTIC CONTINUATION TO THE UNPHYSICAL SHEET OF THE RESOLVENT KERNEL ASSOCIATED WITH THE SCHROEDINGER OPERATOR

1967 ◽  
Vol 18 (1) ◽  
pp. 219-231 ◽  
Author(s):  
J. B. McLEOD
Keyword(s):  
Analytic Continuation ◽  
Schroedinger Operator ◽  
Resolvent Kernel ◽  
Unphysical Sheet

SEMIFACTORIZATION OF THE MULTIDIMENSIONAL SCHROEDINGER OPERATOR

1989 ◽  
Vol 50 (C3) ◽  
pp. C3-87-C3-88
Author(s):  
A. CSIZMAZIA
Keyword(s):  
Schroedinger Operator

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

scholarly journals Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions

2005 ◽  
Vol 614 (1-2) ◽  
pp. 53-61 ◽  
Author(s):  
Johannes Blümlein ◽  
Sven-Olaf Moch
Keyword(s):  
Analytic Continuation ◽  
Anomalous Dimensions

scholarly journals Spectral Inclusion and Analytic Continuation

1999 ◽  
Vol 31 (6) ◽  
pp. 722-728 ◽  
Author(s):  
A. Atzmon ◽  
A. Eremenko ◽  
M. Sodin
Keyword(s):  
Analytic Continuation ◽  
Spectral Inclusion

Analytic continuation of quantum systems and their temporal evolution

1993 ◽  
Vol 47 (6) ◽  
pp. 2602-2614 ◽  
Author(s):  
E. C. G. Sudarshan ◽  
Charles B. Chiu
Keyword(s):  
Analytic Continuation ◽  
Temporal Evolution ◽  
Quantum Systems

Analytic continuation of Matsubara Green's functions

1998 ◽  
Vol 63 (1-3) ◽  
pp. 655-657 ◽  
Author(s):  
E.G. Klepfish ◽  
C.E. Creffield ◽  
E.R. Pike
Keyword(s):  
Analytic Continuation ◽  
Green's Functions ◽  
Green’S Functions
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