| 1. | Interpolation of periodic functions by harmonic functions is accomplished by Fourier transform.
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| 2. | Any harmonic function on a compact connected Riemannian manifold is a constant.
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| 3. | Instead, they resolve to different chords with the same harmonic functions.
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| 4. | However, this loses the connection with harmonic functions.
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| 5. | In several ways, the harmonic functions are real analogues to holomorphic functions.
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| 6. | The uniform limit of a convergent sequence of harmonic functions is still harmonic.
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| 7. | Harmonic functions are the classical example to which the strong maximum principle applies.
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| 8. | Harmonic functions that arise in physics are determined by their Liouville's theorem.
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| 9. | Also, the sum of any two harmonic functions will yield another harmonic function.
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| 10. | Also, the sum of any two harmonic functions will yield another harmonic function.
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