| 21. | The constant of integration follows from the fact that the derivative of a constant function is 0.
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| 22. | This is similar to the fact the a constant function is one whose derivative is constantly 0.
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| 23. | It is the ( trivial ) constant function and every " x " is a root.
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| 24. | Therefore, the Lanczos interpolation of a discrete signal with constant samples does not yield a constant function.
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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. | Suppose is a compact Hausdorff space and is a subalgebra of which contains a non-zero constant function.
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| 27. | If U is a connected set, then the constant functions are the only antiderivatives of the zero function.
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| 28. | By standard differentiation rules, if a polynomial of degree is differentiated times, then it becomes a constant function.
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| 29. | Consequently, the kernel of \ frac { d } { dx } is the space of all constant functions.
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| 30. | The first reason is that the constant function is not normalizable, and thus is not a proper probability distribution.
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