Higher order self-adjoint operators with polynomial coefficients
Mustafa, Muhammad Tahir
Texas State University, Department of Mathematics
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.
Self-adjoint operators, Polynomial coefficients
Azad, H., Laradji, A., & Mustafa, M. T. (2017). Higher order self-adjoint operators with polynomial coefficients. <i>Electronic Journal of Differential Equations, 2017</i>(22), pp. 1-21.