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Homework Help: Differential geometry question

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    A function F of n real variables is called homogeneous of degree r if it satisfies
    F(tx_1, tx_2, ..., tx_n) = (t^r)F(x_1,x_2,...,x_n)

    By differentiation with respect to t, show that a function F is an eigenfunction of the operator:

    x^1 ∂/∂x_1 + ... + x^n ∂/∂x_n

    and find the eigenvalue

    2. Relevant equations

    3. The attempt at a solution
    Here's what I've done so far:

    Differentiating with respect to t:

    dF(tx)/dt = rt^(r-1)F(x)

    But what do they mean by asking me to show it is an eigenfunction of the operator, and how would I go about calculating the eigenvalue? Any hints in the right direction would be super!

  2. jcsd
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