parametrix meaning in Hindi

Examples

1. A suitable truncation of the power series then yields a parametrix.
2. It is sometimes possible to construct a fundamental solution from a parametrix by iteratively improving it.
3. The use of Fredholm operators in partial differential equations is an abstract form of the parametrix method.
4. A parametrix for a differential operator is often easier to construct than a fundamental solution, and for many purposes is almost as good.
5. If is a pseudo-differential operator and is a parametrix, this gives a right inverse to, in other words a fundamental solution, provided that is " small enough " which in practice means that it should be a sufficiently good smoothing operator.
6. The parametrix is a useful concept in the study of elliptic differential operators and, more generally, of hypoelliptic pseudodifferential operators with variable coefficient, since for such operators over appropriate domains a parametrix can be shown to exist, can be somewhat easily constructed and be a smooth function away from the origin.
7. The parametrix is a useful concept in the study of elliptic differential operators and, more generally, of hypoelliptic pseudodifferential operators with variable coefficient, since for such operators over appropriate domains a parametrix can be shown to exist, can be somewhat easily constructed and be a smooth function away from the origin.
8. Having found the analytic expression of the parametrix, it is possible to compute the solution of the associated fairly general elliptic partial differential equation by solving an associated Fredholm integral equation : also, the structure itself of the parametrix reveals properties of the solution of the problem without even calculating it, like its smoothness and other qualitative properties.
9. Having found the analytic expression of the parametrix, it is possible to compute the solution of the associated fairly general elliptic partial differential equation by solving an associated Fredholm integral equation : also, the structure itself of the parametrix reveals properties of the solution of the problem without even calculating it, like its smoothness and other qualitative properties.