On Regular Operator Approximation Theory

On Generalization of Sturm-Liouville Theory for Fractional Bessel Operator

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

Operator Theory on Noncommutative Varieties

We develop a dilation theory for row contractions T := [T1, . . . , Tn] subject to constraints such as p(T1, . . . , Tn) = 0, p ∈ P , where P is a set of noncommutative polynomials. The model n-tuple is the universal row contraction [B1, . . . , Bn] satisfying the same constraints as T , which turns out to be, in a certain sense, the maximal constrained piece of the n-tuple [S1, . . . , Sn] of ...

A Pragmati Approximation Operator

Operator Theory and Operator Algebras

A Sparse Regular Approximation Lemma

We introduce a new variant of Szemerédi’s regularity lemma which we call the sparse regular approximation lemma (SRAL). The input to this lemma is a graph G of edge density p and parameters , δ, where we think of δ as a constant. The goal is to construct an -regular partition of G while having the freedom to add/remove up to δ|E(G)| edges. As we show here, this weaker variant of the regularity ...