5 problems

Let ${\bf A}$ be a semi-bounded self-adjoint operator in a Hilbert space $\mathcal{H}$, and let $\lambda$ be an eigenvalue of ${\bf A}$ with multiplicity $m$. Let ${\bf A}_r$ be th…

Let $A$ be a closed semi-bounded symmetric operator, let ${\bf A}$ denote the associated operator, and let ${\bf A}_F$ be its Friedrichs self-adjoint extension. For…

Let ${\bf L}^n$ be a self-adjoint operator defined by left-definite theory on $L^2[(a,b),w]$ with domain $\mathcal{D}_{\bf L}^n$ that includes a complete system of orthogonal polyn…

Left-definite domain equality conjecture. For every $n\in\mathbb{N}$,

Legendre-function conjecture. These Legendre polynomials can be used as GKN conditions to define the $n/2$ left-definite domain, and together the $2n$ functions constitute a basis…