Electron. J. Differential Equations, Vol. 2017 (2017), No. 22, pp. 1-21.

Higher order self-adjoint operators with polynomial coefficients

Hassan Azad, Abdallah Laradji, Muhammad Tahir Mustafa

Abstract:
We study algebraic and analytic aspects of self-adjoint operators of order four or higher with polynomial coefficients. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain many examples up to order 8; similar examples can be constructed for all even order operators. In particular, a complete classification of all order 4 operators is given.

Submitted October 21, 2016. Published January 18, 2017.
Math Subject Classifications: 33C45, 34A05, 34A30, 34B24, 42C05.
Key Words: Self-adjoint operators; polynomial coefficients.

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  Hassan Azad
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Dhahran 31261, Saudi Arabia
email: hassanaz@kfupm.edu.sa
  Abdallah Laradji
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Dhahran 31261, Saudi Arabia
email: alaradji@kfupm.edu.sa
Muhammad Tahir Mustafa
Department of Mathematics, Statistics and Physics
Qatar University
Doha 2713, Qatar
email: tahir.mustafa@qu.edu.qa

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