Electron. J. Diff. Eqns., Vol. 2005(2005), No. 38, pp. 1-9.

Deficiency indices of a differential operator satisfying certain matching interface conditions

Pallav Kumar Baruah, M. Venkatesulu

A pair of differential operators with matching interface conditions appears in many physical applications such as: oceanography, the study of step index fiber in optical fiber communication, and one dimensional scattering in quantum theory. Here we initiate the study the deficiency index theory of such operators which precedes the study of the spectral theory.

Submitted October 7, 2004. Published March 29, 2005.
Math Subject Classifications: 34B10.
Key Words: Ordinary differential operators; Green's formula; deficiency index; formal selfadjoint boundary-value problems; boundary form; deficiency space.

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Pallav Kumar Baruah
Department of Mathematics and Computer Science
Sri Sathya Sai Institute of Higher Learning
Prasanthinilayam, India
email: baruahpk@yahoo.com
M. Venkatesulu
Department of Computer Applications
Arulmigu Kalasalingam College of Engineering
Virudhunagar (District), Tamil Nadu, India
email: venkatesulu_m2000@yahoo.co.in

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