Pole term decomposition of the resolvent kernel in Fredholm’s form

1987 ◽  
Vol 28 (11) ◽  
pp. 2677-2682 ◽  
Author(s):  
Yoshiko Matsui
Keyword(s):  
Pole Term ◽  
Resolvent Kernel

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 INFRARED FIXED POINT IN THE STRONG RUNNING COUPLING: UNRAVELING THE ΔI = 1/2 PUZZLE IN K-DECAYS

2013 ◽  
Vol 28 (25) ◽  
pp. 1360010 ◽  
Author(s):  
R. J. CREWTHER ◽  
LEWIS C. TUNSTALL
Keyword(s):  
Fixed Point ◽  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Quark Condensate ◽  
Low Energy ◽  
Pole Term ◽  
Leading Order ◽  
Goldstone Bosons ◽  
Running Coupling ◽  
Scale Perturbation

In this paper, we present an explanation for the ΔI = 1/2 rule in K-decays based on the premise of an infrared fixed point α IR in the running coupling αs of quantum chromodynamics (QCD) for three light quarks u, d, s. At the fixed point, the quark condensate [Formula: see text] spontaneously breaks scale and chiral SU (3)L× SU (3)R symmetry. Consequently, the low-lying spectrum contains nine Nambu–Goldstone bosons: π, K, η and a QCD dilaton σ. We identify σ as the f0(500) resonance and construct a chiral-scale perturbation theory χPTσ for low-energy amplitudes expanded in αs about α IR . The ΔI = 1/2 rule emerges in the leading order of χPTσ through a σ-pole term KS→σ→ππ, with a gKSσ coupling fixed by data on γγ→π0π0 and KS→γγ. We also determine R IR ≈5 for the nonperturbative Drell–Yan ratio at α IR .

scholarly journals The resolvent kernel for PCF self-similar fractals

2010 ◽  
Vol 362 (08) ◽  
pp. 4451-4479 ◽  
Author(s):  
Marius Ionescu ◽  
Erin P. J. Pearse ◽  
Luke G. Rogers ◽  
Huo-Jun Ruan ◽  
Robert S. Strichartz
Keyword(s):  
Resolvent Kernel ◽  
Self Similar

scholarly journals Fast quantitative microwave imaging with resolvent kernel extracted from measurements

2015 ◽  
Vol 31 (4) ◽  
pp. 045007 ◽  
Author(s):  
S Tu ◽  
J J McCombe ◽  
D S Shumakov ◽  
N K Nikolova
Keyword(s):  
Microwave Imaging ◽  
Resolvent Kernel
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