Two singular point linear Hamiltonian systems with an interface condition

✍ Scribed by Horst Behncke; Don Hinton

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 165 KB
• Volume: 283
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200910032

✦ Synopsis

Abstract

We consider the problem of a linear Hamiltionian system on ℝ with an interface condition which we take to be at x = 0. Assuming limit point conditions at ±∞, we prove the problem is uniquely solvable, and a resolvent is constructed. Our method of solution is to map the problem onto a half line problem of double size and apply the theory of half line problems. A Titchmarsh‐Weyl function is associated with the problem, and a unitary transform is constructed which maps the differential operator onto the multiplication operator in the Hilbert space determined by the spectral function ρ (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)