Heat Equations in R

  title={Heat Equations in R},
  author={ANDREW S. RAICH},
  • Published 2008
C Hτp(s, z, w)f(w) dw, and our goal is to understand the regularity and pointwise bounds of Hτp and its derivatives. We show that the heat kernel Hτp(s, z, w) is smooth away from the diagonal {(s, z, w) : s = 0, z = w} and our main result is that: Theorem 1. Let p be a subharmonic, nonharmonic polynomial and τ > 0 a parameter. If n ≥ 0 and Y α is a product of |α| operators Y = Z̄τp or Zτp when acting in z and (Zτp) or (Z̄τp) when acting in w, there exist constants c, c1 > 0 independent of τ so… CONTINUE READING

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