7 papers
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 self-adjoint boundary conditions for singular Sturm-Liouville operators bounded from below
Fritz Gesztesy, Lance L. Littlejohn, Roger Nichols
We extend the classical boundary values \begin{align*} & g(a) = - W(u_{a}(λ_0,.), g)(a) = \lim_{x \downarrow a} \frac{g(x)}{\hat u_{a}(λ_0,x)}, \\ &g^{[1]}(a) = (p g')(a) = W(\hat…
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…
Trace formulas applied to the Riemann -function
Mark S. Ashbaugh, Fritz Gesztesy, Lotfi Hermi +3
We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at…