Weyl Function of Sturm–Liouville Problems with Transmission Conditions at Finite Interior Points

2017 ◽  
Vol 14 (5) ◽  
Author(s):  
Kun Li ◽  
Jiong Sun ◽  
Xiaoling Hao
Keyword(s):  
Weyl Function ◽  
Transmission Conditions ◽  
Sturm Liouville ◽  
Interior Points

scholarly journals Dissipative Sturm-Liouville Operators with Transmission Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hüseyin Tuna ◽  
Aytekin Eryılmaz
Keyword(s):  
Transmission Conditions ◽  
Sturm Liouville ◽  
Liouville Operators

In this paper we study dissipative Sturm-Liouville operators with transmission conditions. By using Pavlov’s method (Pavlov 1947, Pavlov 1981, Pavlov 1975, and Pavlov 1977), we proved a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative Sturm-Liouville operators with transmission conditions.

Discontinuous fractional Sturm–Liouville problems with transmission conditions

2019 ◽  
Vol 350 ◽  
pp. 1-10
Author(s):  
Zülfigar Akdoğan ◽  
Ali Yakar ◽  
Mustafa Demirci
Keyword(s):  
Transmission Conditions ◽  
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).

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