scholarly journals Boundary value problems for elliptic differential operators of first order

2012 ◽  
Vol 17 (1) ◽  
pp. 1-78 ◽  
Author(s):  
Werner Ballmann ◽  
Christian Bär
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
First Order ◽  
Elliptic Differential Operators

scholarly journals GREEN'S FUNCTIONS AND REGULARIZED TRACES OF STURM–LIOUVILLE OPERATORS ON GRAPHS

2008 ◽  
Vol 51 (2) ◽  
pp. 315-335 ◽  
Author(s):  
Sonja Currie ◽  
Bruce A. Watson
Keyword(s):  
Boundary Value Problems ◽  
Green's Functions ◽  
Differential Operators ◽  
Green’S Functions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value ◽  
Elliptic Differential Operators ◽  
Sturm Liouville ◽  
Inverse Spectral

AbstractAsymptotic approximations to the Green's functions of Sturm–Liouville boundary-value problems on graphs are obtained. These approximations are used to study the regularized traces of the differential operators associated with these boundary-value problems. Various inverse spectral problems for Sturm–Liouville boundary-value problems on graphs resembling those considered in Halberg and Kramer's ‘A generalization of the trace concept' (Duke Mathematics Journal27 (1960), 607–617), for Sturm–Liouville problems, and Pielichowski's ‘An inverse spectral problem for linear elliptic differential operators' (Universitatis Iagellonicae Acta Mathematica27 (1988), 239–246), for elliptic boundary-value problems, are solved.

scholarly journals On sampling expansions of Kramer type

2004 ◽  
Vol 2004 (5) ◽  
pp. 371-385
Author(s):  
Anthippi Poulkou
Keyword(s):  
Boundary Value Problems ◽  
Discrete Spectrum ◽  
Differential Operators ◽  
Boundary Value ◽  
Sampling Theorem ◽  
Second Order ◽  
Joint Work ◽  
First Order ◽  
Survey Paper ◽  
Sampling Expansions

We treat some recent results concerning sampling expansions of Kramer type. The linkof the sampling theorem of Whittaker-Shannon-Kotelnikov with the Kramer sampling theorem is considered and the connection of these theorems with boundary value problems is specified. Essentially, this paper surveys certain results in the field of sampling theories and linear, ordinary, first-, and second-order boundary value problems that generate Kramer analytic kernels. The investigation of the first-order problems is tackled in a joint work with Everitt. For the second-order problems, we refer to the work of Everitt and Nasri-Roudsari in their survey paper in 1999. All these problems are represented by unbounded selfadjoint differential operators on Hilbert function spaces, with a discrete spectrum which allows the introduction of the associated Kramer analytic kernel. However, for the first-order problems, the analysis of this paper is restricted to the specification of conditions under which the associated operators have a discrete spectrum.

Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

2020 ◽  
Vol 28 (2) ◽  
pp. 237-241
Author(s):  
Biljana M. Vojvodic ◽  
Vladimir M. Vladicic
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

Sign in / Sign up

Export Citation Format

Share Document