arXiv subjects

Agniva Chatterjee

Publications and source records attributed to Agniva Chatterjee.

3 recordsLinked to original sources

arXiv2026

Holomorphic Interpolation of Multivariate Completely Monotone Functions

The integral representation of completely monotone functions of several real variables as Laplace or Stieltjes-Fantappi\'e transforms of positive measures opens a Hilbert space path toward their finite-point interpolation by simpler functions. We combine, within a non-commutative Radon transform framework, the matrix pencil realization of the positive semi-definite Hankel kernel associated with the sampling of a completely monotone function with Weyl's operational calculus and Fantappi\`e's analytic calculus. The interpolation is achieved by finitely determined entire or rational functions, respectively, which are directionally completely monotone. In our relaxation scheme, the original positive measure is approximated by a sequence of specific Wigner distributions, which can also be regarded as analytic functionals. Throughout the interpolation process, tight bounds are enforced on the modulus or the real part of the holomorphic extension to the underlying tube domain.

math.FA↗

arXiv2025

Dual realizations of Bergman spaces on strongly convex domains

The Fantappi\`e and Laplace transforms realize isomorphisms between analytic functionals supported on a convex compact set $K\subset{\mathbb C}^n$ and certain spaces of holomorphic functions associated with $K$. Viewing the Bergman space of a bounded domain in ${\mathbb C}^n$ as a subspace of the space of analytic functionals supported on its closure, the images of the restrictions of these transforms have been studied in the planar setting. For the Fantappi\`e transform, this was done for simply connected domains (Napalkov Jr--Yulumukhamtov, 1995), and for the Laplace transform, this was done for convex domains (Napalkov Jr--Yulumukhamtov, 2004). In this paper, we study this problem in higher dimensions for strongly convex domains, and establish duality results analogous to the planar case. We also produce examples to show that the planar results cannot be generalized to all convex domains in higher dimensions.

math.CV↗

arXiv2024

The Laplace and Leray transforms on some (weakly) convex domains in $\mathbb{C}^2$

The space of Laplace transforms of holomorphic Hardy-space functions have been characterized as weighted Bergman spaces of entire functions in two cases: that of planar convex domains (Lutsenko--Yumulmukhametov, 1991), and that of strongly convex domains in higher dimensions (Lindholm, 2002). In this paper, we establish such a Paley--Weiner result for a class of (weakly) convex Reinhardt domains in $\mathbb{C}^2$ that are well-modelled by the so-called egg domains. We consider Hardy spaces on these domains with respect to a canonical choice of boundary Monge--Ampere measure. This class of domains was introduced by Barrett--Lanzani (2009) to study the $L^2$-boundedness of the Leray transform in the absence of either strongly convexity or $\mathcal{C}^2$-regularity. The boundedness of the Leray transform plays a crucial role in understanding the image of the Laplace transform. As a supplementary result, we expand the known class of convex Reinhardt domains for which the Leray transform is $L^2$-bounded (with respect to the aforementioned choice of boundary measure). Finally, we also produce an example to show that the Lutsenko--Yumulmukhametov result cannot be expected to generalize to all convex domains in higher dimensions.

math.CV↗