elliptic differential operator sentence in Hindi
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- The index of an elliptic differential operator obviously vanishes if the operator is self adjoint.
- Most version of the index theorem can be extended from elliptic differential operators to elliptic pseudodifferential operators.
- Further, she studied the index theory of elliptic differential operators and generalizations of this to equivariant cohomology.
- The equation has also been studied from the point of view of symmetric spaces, and elliptic differential operators.
- In the 1980s, he discovered how to characterize high order approximation problems using the properties of corresponding elliptic differential operators.
- Related problems can be formulated for the Dirichlet problem for the Laplacian on domains in higher dimensions or on Riemannian manifolds, as well as for other elliptic differential operators such as the Cauchy Riemann operator or Dirac operator.
- This theorem can be interpreted in many ways; perhaps one of the most far-reaching has been as the index theorem for an elliptic differential operator on, one of the simplest cases of the Atiyah-Singer index theorem.
- An important consequence is that the kernel of " D " is finite-dimensional, because all eigenspaces of compact operators, other than the kernel, are finite-dimensional . ( The pseudoinverse of an elliptic differential operator is almost never a differential operator.
- Pseudodifferential operators have an order, which can be any real number or even " ", and have symbols ( which are no longer polynomials on the cotangent space ), and elliptic differential operators are those whose symbols are invertible for sufficiently large cotangent vectors.
- 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.
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