On differentiability and analyticity of positive definite functions

@article{Buescu2011OnDA,
  title={On differentiability and analyticity of positive definite functions},
  author={J. Buescu and A. Paixao},
  journal={Journal of Mathematical Analysis and Applications},
  year={2011},
  volume={375},
  pages={336-341}
}
  • J. Buescu, A. Paixao
  • Published 2011
  • Mathematics
  • Journal of Mathematical Analysis and Applications
  • We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is… CONTINUE READING
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