Sentence examples for operator of order from inspiring English sources

Let p be the principal symbol of a hyperbolic (pseudo) differential operator of order m admitting at most double characteristic roots.

Let P(D) be a nonnegative homogeneous elliptic operator of order 2m with real constant coefficients on Rn and V be a suitable real measurable function.

These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1<α≤2.

Precisely, there exists a unitary equivalenceΔ=R+Q−1where [R, Q−1]=0, where the spectrum ofRlies on an arithmetic progression and whereQ−1is a pseudodifferential operator of order −1.

We show that the Laplacian acts as one would expect an elliptic pseudodifferential operator of order d+1 on a space of dimension d to act, where d is determined by the growth rate of the measure of metric balls.

Let us consider the partial differential operator of order.

Here, is called the Bernstein operator of order for.

For and, the weighted -Bernstein operator of order for is defined by (1.1).

Here, I q denotes the Riemann-Liouville fractional integral operator of order q.

The Riemann-Liouville fractional integral operator of order, of a function is defined as (2.2).

where D m is the classical differential operator of order m.