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 Experience-expectant development of contour integration mechanisms in human visual cortex

10.1167/5.2.3 ◽  
2005 ◽  
Vol 5 (2) ◽  
pp. 3 ◽  
Author(s):  
Anthony M. Norcia ◽  
Vanitha Sampath ◽  
Hou Chuan ◽  
Mark W. Pettet
Keyword(s):  
Visual Cortex ◽  
Contour Integration ◽  
Human Visual Cortex ◽  
Integration Mechanisms

scholarly journals Some Mathematical Approaches of Illuminance Calculation by Contour Integration

1992 ◽  
Vol 76 (Appendix) ◽  
pp. 48-49
Author(s):  
Takasi Higo ◽  
Yukitaka Shinoda ◽  
Yoshio Sasaki
Keyword(s):  
Contour Integration

Two-centre Coulomb integrals over STOs from analytical evaluation of k-integrals by contour integration in the complex plane

1990 ◽  
Vol 167 (6) ◽  
pp. 547-554 ◽  
Author(s):  
Giuseppe Figari ◽  
Camilla Costa ◽  
Roberto Pratolongo ◽  
Valerio Magnasco
Keyword(s):  
Complex Plane ◽  
Contour Integration ◽  
Analytical Evaluation ◽  
Coulomb Integrals

scholarly journals Both predictability and familiarity facilitate contour integration

2014 ◽  
Vol 14 (5) ◽  
pp. 11-11 ◽  
Author(s):  
M. Sassi ◽  
M. Demeyer ◽  
B. Machilsen ◽  
T. Putzeys ◽  
J. Wagemans
Keyword(s):  
Contour Integration
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