41. The index notation for the dot and cross products carries over to the differential operators of vector calculus. 42. The motivation for their study is that their homomorphisms correspond to invariant differential operators over generalized flag manifolds. 43. Further, she studied the index theory of elliptic differential operators and generalizations of this to equivariant cohomology. 44. For the gradient in other orthogonal coordinate systems, see Orthogonal coordinates ( Differential operators in three dimensions ). 45. One case for non-commutative rings where localization has a clear interest is for rings of differential operators . 46. Any differential operator exhibiting this property is called a hypoelliptic operator; thus, every elliptic operator is hypoelliptic. 47. For general quantity "'M "'they act as grade lowering and raising differential operators . 48. This formula can be used to derive a formula that computes the symbol of the composition of differential operators . 49. I am a mathematician, with some knowledge about spectra of differential operators , which this article is about. 50. By means of the Fourier transform, pseudo-differential operators can be defined which allow for fractional calculus.
