6 papers
Holomorphic Interpolation of Multivariate Completely Monotone Functions
Mainak Bhowmik, Agniva Chatterjee, Mihai Putinar
The integral representation of completely monotone functions of several real variables as Laplace or Stieltjes-Fantappié transforms of positive measures opens a Hilbert space path…
A family of tetrablock contractions with non-commuting fundamental operators
Mainak Bhowmik
In this note, we provide a family of tetrablock contractions that have tetrablock isometric dilation, but the corresponding fundamental operators do not commute. This a…
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…
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…
Function theory on quotient domains related to the polydisc
Mainak Bhowmik, Poornendu Kumar
Inner functions are the backbone of holomorphic function theory. This paper studies the inner functions on quotient domains of the open unit polydisc, $\bD^d$, arising from the gro…
Herglotz representation for operator-valued function on a set associated with test functions
Mainak Bhowmik, Poornendu Kumar
The Herglotz representation theorem for holomorphic functions with non-negative real part is a fundamental result in the theory of holomorphic functions. In this paper, we reinterp…