Sentence examples for be a differential operator from inspiring English sources

Let P be a differential operator with analytic coefficients and elliptic, or more generally of principal type and hypoelliptic, in an open Ω of Rn and let (kj) be an increasing sequence of positive integers.

Let be a differential operator generated by problem (3.1 - 3.2 3.1 - 3.2hat is, (3.6).

Let Q be a differential operator in L p ( R n ; l q ), generated by problem (5.7) and B = B ( L p ( R n ; l q ) ). Applying Theorem 3.7, we have the following.

Let Q be a differential operator in (L_{p,gamma } ( R^{n};l_{q} ) ) generated by problem (6.1) and B=B bigl( L_{p,gamma } bigl( R^{n};l_{q} bigr) bigr).

Our main result is the positive commutator estimateχI(H2Δg)i2[H2Δg,A]χI(H2Δg)⩾CχI(H2Δg 2, where H↑∞ is a large parameter, I is a compact interval in (0,∞), and χI its indicator function, and where A is a differential operator supported outside a compact set and equal to (1/2)(rDr+ rDr)∗) near infinity.

We study spectral and propagation properties of operators of the form Sh = ∑Nj=0hjPj where ∀ j P j is a differential operator of order j on a manifold M, asymptotically as h → 0. The estimates are in terms of the flow {φt} of the classical Hamiltonian H x, p) = ∑Nj=0 σPj x, p) on T*M, where σPj, is the principal symbol of P j.

where is a differential operator, whose coefficients have compact support in a neighborhood of the origin.

In this case, A is a differential operator of the same order K.

Note that (L_{11}) is a differential operator in (frac{partial }{partial s},frac{partial }{partial y_k},1le kle n-1).

The pull-back is a linear isomorphism of onto for every and of onto for every Meanwhile, where is a differential operator of order with coefficients of class on and where is a differential operator of order with coefficients of class on.

Here A ( x, D ) is a differential operator of order 2m, C ( x, D ) is a column of boundary operators C 1, …, C m, and λ is a complex parameter.