6 papers · 1 filter
Left-Definite Variations of the Classical Fourier Expansion Theorem, Part II
Lance L. Littlejohn, Edward L. Smith, Anton Zettl
In 2002, Littlejohn and Wellman developed a general left-definite theory for arbitrary self-adjoint operators in a Hilbert space that are bounded below by a positive constant. Zett…
Interlacing of zeros of Laguerre polynomials of equal and consecutive degree
J. Arvesú, K. Driver, L. Littlejohn
We investigate interlacing properties of zeros of Laguerre polynomials and where and . W…
A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements
Fritz Gesztesy, Lance L. Littlejohn, Isaac Michael +1
The principal aim of this paper is to extend Birman's sequence of integral inequalities originally obtained in 1961, and containing Hardy's and Rellich's inequality as special case…
A New Spectral Analysis of the Sixth-order Krall Differential Expression
K. Elliott, L. L. Littlejohn, R. Wellman
In this paper, we construct a self-adjoint operator T generated by the sixth-order Krall differential expression in the extended Hilbert space L^2(-1,1) + C^2. To obtain T, we appl…
On Weighted Hardy-Type Inequalities
Chian Yeong Chuah, Fritz Gesztesy, Lance L. Littlejohn +3
We revisit weighted Hardy-type inequalities employing an elementary ad hoc approach that yields explicit constants. We also discuss the infinite sequence of power weighted Birman-H…
Differential operator for discrete Gegenbauer--Sobolev orthogonal polynomials: eigenvalues and asymptotics
Lance L. Littlejohn, Juan F. Mañas-Mañas, Juan J. Moreno--Balcázar +1
We consider the following discrete Sobolev inner product involving the Gegenbauer weight $$(f,g)_S:=\int_{-1}^1f(x)g(x)(1-x^2)^αdx+M\big[f^{(j)}(-1)g^{(j)}(-1)+f^{(j)}(1)g^{(j)}(1)…