6 papers
On Sesquilinear Forms for Lower Semibounded (Singular) Sturm-Liouville Operators
Jussi Behrndt, Fritz Gesztesy, Seppo Hassi +2
Any self-adjoint extension of a (singular) Sturm-Liouville operator bounded from below uniquely leads to an associated sesquilinear form. This form is characterized in terms of pri…
A generalized Birman-Schwinger principle and applications to one-dimensional Schrödinger operators with distributional potentials
Fritz Gesztesy, Roger Nichols
Given a self-adjoint operator bounded from below in a complex Hilbert space , the corresponding scale of spaces $\mathcal{H}_{+1}(H_0) \subset \mathcal{H} \subse…
Some Remarks on the Product Formula for Defect Numbers of Closed Operators
Christoph Fischbacher, Fritz Gesztesy, Lance L. Littlejohn
This largely pedagogical paper recalls some facts on defect numbers of products of closed operators employing results from the theory of semi-Fredholm operators and then applies th…
Optimal Power-Weighted Birman--Hardy--Rellich-type Inequalities on Finite Intervals and Annuli
Fritz Gesztesy, Michael M. H. Pang
We derive an optimal power-weighted Hardy-type inequality in integral form on finite intervals and subsequently prove the analogous inequality in differential form. We note that th…
Factorizations and Power Weighted Rellich and Hardy--Rellich-Type Inequalities
Fritz Gesztesy, Michael M. H. Pang, Jake Parmentier +1
We revisit and extend a variety of inequalities related to power weighted Rellich and Hardy--Rellich inequalities, including an inequality due to Schmincke.
Logarithmic Refinements of a Power Weighted Hardy--Rellich-Type Inequality
Fritz Gesztesy, Michael M. H. Pang, Jonathan Stanfill
The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy--Rellich inequality on -dimensional balls, valid for the largest variety of u…