differential operator

The most common differential operator is the action of taking the derivative itself.

We next give the example of differential operators with constant coefficients.

The exponential over a differential operator is understood as a power series.

He has made notable contributions to the study of partial differential operators.

Now, we must continue the differential operator to the central point x in the punctured neighborhood.

This extension of the above differential operator need not be constrained only to real powers.

Similar differential operators can be applied to the fields, to find:

The momentum operator is an example of a differential operator.

This turns out not to be a full differential operator in the usual sense but has many of the desired properties.

In connection with differential operators it is common to use inner products and integration by parts.

The reason for this is that for many purposes there are not enough differential operators.

Higher derivatives and algebraic differential operators can also be defined.

These are differential operators, except for potential energy V which is just a multiplicative factor.

The idea is that a velocity field can also be understood as a first order differential operator acting on functions.

The symbol of a differential operator has broad applications to Fourier analysis.

Thus under certain conditions, one may interchange the integral and partial differential operators.

One can show that the corresponding action of Lie algebra is given by the differential operators and respectively.

For general quantity M they act as grade lowering and raising differential operators.

Any polynomial in D with function coefficients is also a differential operator.

This is almost the simplest possible partial differential operator with non-constant coefficients.

A module over a ring of differential operators.

The approach is global in character, and differs from the functional analysis techniques traditionally used to study differential operators.

The analysis of these problems involves the eigenfunctions of a differential operator.

Here, L stands for a linear differential operator.

A D-module is an algebraic structure with several differential operators acting on it.