HIGHER ORDER SELF-ADJOINT OPERATORS WITH POLYNOMIAL COEFFICIENTS

被引：0

作者：

Azad, Hassan ^{[1
]}

Laradji, Abdallah ^{[1
]}

Mustafa, Muhammad Tahir ^{[2
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] Qatar Univ, Dept Math Stat & Phys, Doha 2713, Qatar

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年

关键词：

Self-adjoint operators; polynomial coefficients; KOEKOEKS DIFFERENTIAL-EQUATION; GENERALIZED JACOBI-POLYNOMIALS; ORTHOGONAL POLYNOMIALS; LAGUERRE-POLYNOMIALS; EIGENFUNCTIONS; SYSTEMS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：21

共 27 条

[1] Polynomial solutions of certain differential equations arising in physics [J].

Azad, H. ;

Laradji, A. ;

Mustafa, M. T. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (12) :1615-1624

[2] Polynomial solutions of differential equations [J].

Azad, H. ;

Laradji, A. ;

Mustafa, M. T. .

ADVANCES IN DIFFERENCE EQUATIONS, 2011,

[3] A DIRECT APPROACH TO KOEKOEKS DIFFERENTIAL-EQUATION FOR GENERALIZED LAGUERRE-POLYNOMIALS [J].

BAVINCK, H .

ACTA MATHEMATICA HUNGARICA, 1995, 66 (03) :247-253

[4] Differential operators having Sobolev type Laguerre polynomials as eigenfunctions [J].

Bavinck, H .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (12) :3561-3567

[5] A note on the Koekoeks' differential equation for generalized Jacobi polynomials [J].

Bavinck, H .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 115 (1-2) :87-92

[6] On sturm-liouville polynomial systems [J].

Bochner, S .

MATHEMATISCHE ZEITSCHRIFT, 1929, 29 :730-736

[7]

Brenke WC., 1930, B AM MATH SOC, V36, P77, DOI [DOI 10.1090/S0002-9904-1930-04888-0, 10.1090/s0002-9904-1930- 04888-0]

[8]

Everitt W.N., 1957, Quart. J. Math. Oxford, V8, P146

[9] Orthogonal polynomial solutions of linear ordinary differential equations [J].

Everitt, WN ;

Kwon, KH ;

Littlejohn, LL ;

Wellman, R .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 133 (1-2) :85-109

[10]

Ince E. L., 1956, ORDINARY DIFFERENTIA

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