| 1. | This particular derivative operator has a Green's function:
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| 2. | Where \ nabla represents the flat-space derivative operator.
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| 3. | Where \ mathcal { D } denotes the derivative operator.
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| 4. | Neither the interior derivative operator nor the exterior derivative operator is invertible.
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| 5. | Neither the interior derivative operator nor the exterior derivative operator is invertible.
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| 6. | Note that although the derivative operator is not continuous, it is closed.
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| 7. | In addition to the wedge product, there is also the exterior derivative operator.
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| 8. | This means that is a Green's function for the second derivative operator.
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| 9. | The Laplace operator ? and the partial derivative operator will commute on this class of functions.
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| 10. | With \ boldsymbol { \ nabla } the gradient operator and \ partial _ t the time derivative operator.
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