The Spectral Expansion on the Entire Real Line of Green's Function for a Three-layer Medium in the Fundamental Functions of a Nonself-adjoint Sturm-liouville Operator

PIERS Online ◽  
2006 ◽  
Vol 2 (4) ◽  
pp. 344-346
Author(s):  
Evgeny G. Saltykov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Real Line ◽  
Liouville Operator ◽  
Spectral Expansion ◽  
Entire Real Line ◽  
Layer Medium ◽  
Sturm Liouville

scholarly journals Discontinuous Sturm-Liouville Problems and Associated Sampling Theories

2011 ◽  
Vol 2011 ◽  
pp. 1-30 ◽  
Author(s):  
M. M. Tharwat
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Eigenfunction Expansion ◽  
Green’S Functions ◽  
Transmission Conditions ◽  
Expansion Theorem ◽  
Sampling Theorems ◽  
Sturm Liouville ◽  
Special Case

This paper investigates the sampling analysis associated with discontinuous Sturm-Liouville problems with eigenvalue parameters in two boundary conditions and with transmission conditions at the point of discontinuity. We closely follow the analysis derived by Fulton (1977) to establish the needed relations for the derivations of the sampling theorems including the construction of Green's function as well as the eigenfunction expansion theorem. We derive sampling representations for transforms whose kernels are either solutions or Green's functions. In the special case, when our problem is continuous, the obtained results coincide with the corresponding results in the work of Annaby and Tharwat (2006).

scholarly journals Green's Function Method for Self-Adjoint Realization of Boundary-Value Problems with Interior Singularities

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
K. Aydemir ◽  
O. Sh. Mukhtarov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Resolvent Operator ◽  
Function Method ◽  
Homogeneous Equation ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Existence Conditions ◽  
Special Solutions ◽  
The Resolvent Operator

The purpose of this paper is to investigate some spectral properties of Sturm-Liouville type problems with interior singularities. Some of the mathematical aspects necessary for developing our own technique are presented. By applying this technique we construct some special solutions of the homogeneous equation and present a formula and the existence conditions of Green's function. Furthermore, based on these results and introducing operator treatment in adequate Hilbert space, we derive the resolvent operator and prove self-adjointness of the considered problem.

scholarly journals The Green's function for Caputo fractional boundary value problem with a convection term

2022 ◽  
Vol 7 (4) ◽  
pp. 4887-4897
Author(s):  
Youyu Wang ◽  
◽  
Xianfei Li ◽  
Yue Huang
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Green’S Function ◽  
Green's Function ◽  
Operator Theory ◽  
Fractional Boundary Value Problem ◽  
Convection Term ◽  
New Ideas ◽  
Sturm Liouville ◽  
Fractional Differential

<abstract><p>By using the operator theory, we establish the Green's function for Caputo fractional differential equation under Sturm-Liouville boundary conditions. The results are new, the method used in this paper will provide some new ideas for the study of this kind of problems and easy to be generalized to solving other problems.</p></abstract>

scholarly journals Solution of Ordinary Differential Equation Using Green's Function & Sturm - Liouville Problem

2019 ◽  
pp. 241-244
Author(s):  
S. Angel Auxzaline Mary ◽  
T. Ramesh
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Initial Value Problem ◽  
Series Representation ◽  
Liouville Problem ◽  
Initial Value ◽  
Sturm Liouville

In this paper, we describe Green's function to determine the importance of this function, i.e. Boundary & Initial Value problem, Sturm-Liouville Problem. Along with the series representation of Green's Function.

scholarly journals REGULARIZED GREEN'S FUNCTION FOR THE INVERSE SQUARE POTENTIAL

2002 ◽  
Vol 17 (13) ◽  
pp. 817-826 ◽  
Author(s):  
HORACIO E. CAMBLONG ◽  
CARLOS R. ORDÓÑEZ
Keyword(s):  
Quantum Mechanics ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Real Space ◽  
Liouville Theory ◽  
Hyperspherical Coordinates ◽  
Closed Expression ◽  
Integral Treatment ◽  
Sturm Liouville

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm–Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.

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