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math.SP2017
On Birman's sequence of Hardy-Rellich-type inequalities
Fritz Gesztesy, Lance L. Littlejohn, Isaac Michael +1
In 1961, Birman proved a sequence of inequalities for valid for functions in In particular, i…
math.CA2017
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)…
math.FA2017
Self-Adjoint Operators in Extended Hilbert Spaces : An Application of the General GKN-EM Theorem
Lance Littlejohn, Richard Wellman
We construct self-adjoint operators in the direct sum of a complex Hilbert space and a finite dimensional complex inner product space . The operator theory developed in this…