Kernel operators

Integral Operators Induced by the Fock Kernel

We study the L boundedness and find the norm of a class of integral operators induced by the reproducing kernel of Fock spaces over C.

On Kernel Representation of Linear Operators

Kernel Asymptotics of Exotic Second-Order Operators

The Navier–Lamé operator of classical elasticity, μ∆v+(λ+μ)∇(∇·v), is the simplest example of a linear differential operator whose second-order terms involve a coupling among the components of a vector-valued function. Similar operators on Riemannian manifolds arise in conformal geometry and in quantum gravity. (In the latter context they have come to be called “nonminimal”, but “exotic” is pro...

Degenerate Hypoelliptic Operators and the Gaussian Kernel

Kernel operators and improved inclusion-exclusion bounds

We present a new and elementary proof of some recent improvements of the classical inclusion-exclusion bounds. The key idea is to use an injective mapping, similar to the bijective mapping in Garsia and Milne’s “bijective” proof of the classical inclusion-exclusion principle.