Related papers: Specht's invariant and localization of operator tu…

In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of…

We propose a means by which some categorifications can be evaluated at a root of unity. This is implemented using a suitable localization in the context of prior work by the authors on categorification of the Jones-Wenzl projectors. Within…

Based on Johnson's operator formula for the equivariant Gromov-Witten theory of $\mathbb{P}^1$-orbifolds, we give a new approach to the operator formalism by Okounkov and Pandharipande regarding the $\mathbb{C}^*$-equivariant Gromov-Witten…

There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\C^n$. We introduce a…

Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$…

This paper studies fractional integral operator for vector fields in weighted $L^1$. Using the estimates on fractional integral operator and Stein-Weiss inequalities, we can give a new proof for a class of Caffarelli-Kohn-Nirenberg…

We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the…

Vertex operator realizations of symplectic and orthogonal Schur functions are studied and expanded. New proofs of determinant identities of irreducible characters for the symplectic and orthogonal groups are given. We also give a new proof…

We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of order $k\ge 2$ on a smooth manifold of dimension $n\ge 2$ and show their application to the equivalence…

We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.

We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…

We reexamine equivariant generalizations of the Lefschetz number and Reidemeister trace using categorical traces. This gives simple, conceptual descriptions of the invariants as well as direct comparisons to previously defined…

Because of the nonlocal properties of fractional operators, higher order schemes play more important role in discretizing fractional derivatives than classical ones. The striking feature is that higher order schemes of fractional…

The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-self-adjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that…

We give some new characterizations of almost weak Dunford-Pettis operators and we investigate their relationship with weak Dunford-Pettis operators.

We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…

We characterize the condition $(\Omega)$ for smooth kernels of partial differential operators in terms of the existence of shifted fundamental solutions satisfying certain properties. The conditions $(P\Omega)$ and…

We prove some refinements of an inequality due to X. Zhan in an arbitrary complex Hilbert space by using some results on the Heinz inequality. We present several related inequalities as well as new variants of the Corach--Porta--Recht…

In this expository article, we explain how to use localization to compute Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten invariants of smooth toric Deligne-Mumford stacks.

We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form. We also present an example of unitary equivalence between shifts defined…