scholarly journals Estimates of the Fundamental Solution for Higher Order Schrödinger Type Operators and Their Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Satoko Sugano
Keyword(s):  
Fundamental Solution ◽  
Higher Order ◽  
Schrödinger Type Operators

scholarly journals Riesz Transforms Associated with Higher-Order Schrödinger Type Operators

2017 ◽  
Vol 49 (3) ◽  
pp. 381-410
Author(s):  
Qingquan Deng ◽  
Yong Ding ◽  
Xiaohua Yao
Keyword(s):  
Higher Order ◽  
Riesz Transforms ◽  
Schrödinger Type Operators

REGULARIZATION TECHNIQUES FOR THE METHOD OF FUNDAMENTAL SOLUTIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341004 ◽  
Author(s):  
CSABA GÁSPÁR
Keyword(s):  
Fundamental Solution ◽  
Solution Process ◽  
Partial Differential Operator ◽  
Fundamental Solutions ◽  
Higher Order ◽  
Method Of Fundamental Solutions ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Approximation Theorems ◽  
Regularization Techniques

A special regularization method based on higher-order partial differential equations is presented. Instead of using the fundamental solution of the original partial differential operator with source points located outside of the domain, the original second-order partial differential equation is approximated by a higher-order one, the fundamental solution of which is continuous at the origin. This allows the use of the method of fundamental solutions (MFS) for the approximate problem. Due to the continuity of the modified operator, the source points and the boundary collocation points are allowed to coincide, which makes the solution process simpler. This regularization technique is generalized to various problems and combined with the extremely efficient quadtree-based multigrid methods. Approximation theorems and numerical experiences are also presented.

scholarly journals Spectral Bounds for Polydiagonal Jacobi Matrix Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Arman Sahovic
Keyword(s):  
Jacobi Matrix ◽  
Symmetric Matrix ◽  
Higher Order ◽  
Main Diagonal ◽  
Matrix Operator ◽  
Discrete Schrödinger Operators ◽  
Canonical Relation ◽  
Spectral Bounds ◽  
Schrödinger Type Operators ◽  
Matrix Operators

The research on spectral inequalities for discrete Schrödinger operators has proved fruitful in the last decade. Indeed, several authors analysed the operator’s canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we consider a generalisation of this relation with regard to connecting higher order Schrödinger-type operators with symmetric matrix operators with arbitrarily many nonzero diagonals above and below the main diagonal. We thus obtain spectral bounds for such matrices, similar in nature to the Lieb-Thirring inequalities.

scholarly journals On the approximation of Finsler metrics on Euclidean domains

1999 ◽  
Vol 42 (3) ◽  
pp. 589-609 ◽  
Author(s):  
G. Barbatis
Keyword(s):  
Fundamental Solution ◽  
Parabolic Equations ◽  
Higher Order ◽  
Finsler Metrics ◽  
Higher Order Parabolic Equations ◽  
Euclidean Domains

We prove that Finsler metrics on Euclidean domains can be approximated in a certain sense by so-called Finsler-type metrics. As an application we improve upon previous estimates on the fundamental solution of higher order parabolic equations.

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