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math.CV2025
The multivariate Herglotz-Nevanlinna class: Rational approximation
Mainak Bhowmik, Mihai Putinar
We return to Takagi's variational principle, generalized after forty years to two complex variables by Pfister. Both isolating some extremal rational functions associated to a boun…
math.FA2025
The Multivariate Herglotz-Nevanlinna Class: Superresolution
Mainak Bhowmik, Mihai Putinar
Bounded holomorphic interpolation problems associated to finitely many data have, in general, distinct solutions. Uniqueness arises only in some convex extreme configurations. Rati…