Two-Orthogonal Polynomial Sequences as Eigenfunctions of a Third-Order Differential Operator

2015 ◽  
Vol 13 (2) ◽  
pp. 687-701 ◽  
Author(s):  
T. Augusta Mesquita ◽  
P. Maroni
Keyword(s):  
Differential Operator ◽  
Orthogonal Polynomial ◽  
Order Differential Operator ◽  
Third Order ◽  
Polynomial Sequences

scholarly journals On some connection results between Laguerre polynomials via third-order differential operator

2020 ◽  
Author(s):  
Baghdadi Aloui ◽  
wathek chammam ◽  
Jihad Souissi
Keyword(s):  
Differential Operator ◽  
Laguerre Polynomials ◽  
Order Differential Operator ◽  
Third Order ◽  
Orthogonal Sequence

Let $\{L^{(\alpha)}_n\}_{n\geq 0}$, ($\alpha\neq-m, \ m\geq1$), be the monic orthogonal sequence of Laguerre polynomials. We give a new differential operator, denoted here $\mathscr{L}^{+}_{\alpha}$, raises the degree and also the parameter of $L^{(\alpha)}_n(x)$. More precisely, $\mathscr{L}^{+}_{\alpha}L^{(\alpha)}_n(x)=L^{(\alpha+1)}_{n+1}(x), \ n\geq0$. As an illustration, we give some properties related to this operator and some other operators in the literature, then we give some connection results between Laguerre polynomials via this new operator.

25.—Spectrum of a Third-order Differential Operator with Large Coefficients

1975 ◽  
Vol 72 (4) ◽  
pp. 299-305
Author(s):  
K. Unsworth
Keyword(s):  
Differential Operator ◽  
Differential Expression ◽  
Real Axis ◽  
Sufficient Conditions ◽  
Order Differential Operator ◽  
Third Order ◽  
Minimal Operator ◽  
The Third ◽  
Entire Real Axis

SynopsisThis paper sets out to study the spectrum of self-adjoint extensions of the minimal operator associated with the third-order formally symmetric differential expression. The technique employed is the method of singular sequences. Sufficient conditions are established on the coefficients of the differential expression in order that the spectrum should cover the entire real axis. Particular cases in which the coefficients behave roughly as powers of x as the magnitude of x becomes large are then considered, and certain conclusions are drawn regarding the spectra under different restrictions on these powers of x.

The deficiency indices of a symmetric third-order differential operator

1995 ◽  
Vol 58 (3) ◽  
pp. 1002-1005
Author(s):  
V. R. Mukimov ◽  
Ya. T. Sultanaev
Keyword(s):  
Differential Operator ◽  
Order Differential Operator ◽  
Third Order ◽  
Deficiency Indices

Self-adjoint extensions of singular third-order differential operator and applications

2014 ◽  
Author(s):  
Elgiz Bairamov ◽  
Meltem Sertbaş ◽  
Zameddin I. Ismailov
Keyword(s):  
Differential Operator ◽  
Order Differential Operator ◽  
Third Order

scholarly journals Absolute and uniform convergence of spectral expansion of the function from the class W1p(g), p > 1, in eigenfunctions of third order differential operator

2017 ◽  
Vol 101 (115) ◽  
pp. 169-182
Author(s):  
V.M. Kurbanov ◽  
E.B. Akhundova
Keyword(s):  
Differential Operator ◽  
Convergence Rate ◽  
Uniform Convergence ◽  
Spectral Expansion ◽  
Ordinary Differential Operator ◽  
Order Differential Operator ◽  
Third Order ◽  
Uniform Convergence Rate

We study an ordinary differential operator of third order and absolute and uniform convergence of spectral expansion of the function from the class W1p(G), G = (0,1), p > 1, in eigenfunctions of the operator. Uniform convergence rate of this expansion is estimated.

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