| 21. | In this example one can easily see that pointwise convergence does not preserve differentiability or continuity.
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| 22. | As far as I know, having continuous partial derivatives is strictly a stronger condition than differentiability.
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| 23. | All functions are assumed to be of differentiability class " C " 1 unless otherwise noted.
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| 24. | One notion of continuous differentiability in " U " requires that the mapping on the product space
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| 25. | The problem is that we are talking about exponentials, rather than the differentiability of a constant function.
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| 26. | Finally, since differentiability implies continuity, the contrapositive states " discontinuity " implies non-differentiability.
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| 27. | Finally, since differentiability implies continuity, the contrapositive states " discontinuity " implies non-differentiability.
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| 28. | Space is by definition a continuum, but the assumption of differentiability is not supported by any fundamental reason.
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| 29. | The Riesz transforms arises in the study of differentiability properties of harmonic potentials in potential theory and harmonic analysis.
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| 30. | The assumption of differentiability can be weakened to continuity and one-sided differentiability of " f ".
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