Sentence examples for heat operators from inspiring English sources

In a joint work with R. Seeley, a calculus of weakly parametric pseudodifferential operators on closed manifolds was introduced and used to obtain complete asymptotic expansions of traces of resolvents and heat operators associated with the Atiyah Patodi Singer problem.

We will adopt the spirit of the proof for the heat operator as in [34].

Let (T t,x)) be the fundamental solution of the heat operator (partial_{t}-triangle) in (xin R^{N}).

One of the most important degenerate parabolic operators is the heat operator associated with the subelliptic operator on a Carnot group.

The main difficulty is the complicated expression of the fundamental solution (P t,x)) of the fractional heat operator (partial_{t}+ -triangle)^{frac{beta}{2}}).

Let (P t,x)) be the fundamental solution of the fractional heat operator (partial _{t}+ -triangle)^{frac{beta}{2}}) in (xin R^{N}).

Here we discuss some elementary properties of the fundamental solution (P t,x)) of the fractional heat operator (partial_{t}+ -triangle )^{frac{beta}{2}}).

First, the fundamental solution (P t,x)) of the fractional heat operator (partial _{t}+ -triangle)^{frac{beta}{2}}) is more complicated than the fundamental solution (T(t,x)) of the heat operator (partial _{t}-triangle), this will bring about some obstacles since the fractional power Laplacian is a nonlocal operator.

We consider the generalized Segal Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type.

This extends a result of Ji and Weber [17] where it was shown that under identical conditions the heat operator is subspace-chaotic on these spaces.

In order to prove the stability problems of quartic functional equations in the space of we employ the -dimensional heat kernel, that is, the fundamental solution of the heat operator in given by (47).