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APM346-2016F
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APM346--Lectures
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Chapter 8
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Must harmonic polynomial be homogeneous?
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Topic: Must harmonic polynomial be homogeneous? (Read 3015 times)
Shentao YANG
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Must harmonic polynomial be homogeneous?
«
on:
November 12, 2016, 10:05:03 PM »
Why harmonic polynomial of $deg=n$ must also be homogeneous polynomial of $deg=n$?
Say, $\Delta ({x^2} - {y^2} + z) = 2 - 2 + 0 = 0$, but we do not count $ ({x^2} - {y^2} + z)$ as harmonic polynomial of $deg=2$.
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Victor Ivrii
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Re: Must harmonic polynomial be homogeneous?
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Reply #1 on:
November 13, 2016, 10:08:33 AM »
In general NO, but we are looking at homogeneous polynomials. Obviously if a polynomial is harmonic, then all it homogeneous components are also are harmonic.
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Toronto Math Forum
»
APM346-2016F
»
APM346--Lectures
»
Chapter 8
»
Must harmonic polynomial be homogeneous?