Regular approximation of singular Sturm–Liouville problems with transmission conditions

2014 ◽  
Vol 247 ◽  
pp. 511-520 ◽  
Author(s):  
Maozhu Zhang
Keyword(s):  
Transmission Conditions ◽  
Regular Approximation ◽  
Sturm Liouville

scholarly journals Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Maozhu Zhang ◽  
Kun Li ◽  
Hongxiang Song
Keyword(s):  
Boundary Conditions ◽  
Operator Theory ◽  
Resolvent Convergence ◽  
Spectral Inclusion ◽  
Regular Approximation ◽  
Special Cases ◽  
Abstract Operator ◽  
Norm Resolvent Convergence ◽  
Sturm Liouville ◽  
Spectral Exactness

AbstractIn this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

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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