Two-Dimensional Trace-Normed Canonical Systems of Differential Equations and Selfadjoint Interface Conditions

2005 ◽  
Vol 51 (1) ◽  
pp. 73-108 ◽  
Author(s):  
Henk de Snoo ◽  
Henrik Winkler
Keyword(s):  
Differential Equations ◽  
Two Dimensional ◽  
Interface Conditions ◽  
Canonical Systems ◽  
Systems Of Differential Equations

Canonical systems of differential equations with self-adjoint interface conditions on graphs

2005 ◽  
Vol 135 (2) ◽  
pp. 297-315 ◽  
Author(s):  
Henk de Snoo ◽  
Henrik Winkler
Keyword(s):  
Differential Equations ◽  
Fourier Transformation ◽  
Spectral Representation ◽  
Interface Condition ◽  
Interface Conditions ◽  
Canonical Systems ◽  
Linear Subspaces ◽  
Systems Of Differential Equations ◽  
Explicit Formulae ◽  
Generalized Fourier Transformation

For n canonical systems of differential equations, the corresponding n copies of their domain (0, ∞) are thought of as a graph with vertex 0. An interface condition at 0 is given by a so-called Nevanlinna pair. Explicit formulae are deduced for the spectral representation of the corresponding underlying self-adjoint relation and the generalized Fourier transformation. Furthermore, results on compressions of the Fourier transformation to closed linear subspaces and the multiplicity of the eigenvalues if the spectrum is discrete are presented

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