Say we have ##P_k(z)## a family of entire functions, and they depend analytically on ##k## in ##\Delta##. Assume ##P_k(z)## is nonzero on ##S^1## for all ##k##. How do I see that for each ##t \ge 0##, we have that$$\sum_{|z| < 1, P_k(z) = 0} z^t$$is an analytic function of ##k##? Here, the zeros...
Homework Statement
Consider the real-vector space of polynomials (i.e. real coefficients) ##f(x)## of at most degree ##3##, let's call that space ##X##. And consider the real-vector space of polynomials (i.e. real coefficients) of at most degree ##2##, call that ##Y##. And consider the linear...