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