scholarly journals The analytic continuation of the resolvent kernel and scattering operator associated with the Schroedinger operator

1966 ◽  
Vol 16 (2) ◽  
pp. 311-332 ◽  
Author(s):  
C.L Dolph ◽  
J.B McLeod ◽  
D Thoe
Keyword(s):  
Analytic Continuation ◽  
Scattering Operator ◽  
Schroedinger Operator ◽  
Resolvent Kernel

Scattering operator and Eisenstein integral for Kleinian groups

1990 ◽  
Vol 108 (2) ◽  
pp. 203-217 ◽  
Author(s):  
N. Mandouvalos
Keyword(s):  
Analytic Continuation ◽  
Kleinian Groups ◽  
Scattering Operator ◽  
Exponent Of Convergence

In this paper we study certain aspects of the problem of analytic continuation of the scattering operator and Eisenstein integral which we introduced in [7, 8, 10], for Kleinian groups Γ with exponent of convergence δ(Γ) ≥ 1. The corresponding problem for groups with δ(Γ) < 1 was examined and solved in [9].

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

Focusing and imaging using eigenfunctions of the scattering operator

1997 ◽  
Vol 102 (2) ◽  
pp. 715-725 ◽  
Author(s):  
T. Douglas Mast ◽  
Adrian I. Nachman ◽  
Robert C. Waag
Keyword(s):  
Scattering Operator

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
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