Related papers: Complete Nevanlinna-Pick kernels And The Character…

We prove a negative solution to the analogue of Hilbert's tenth problem for rings of one variable non-Archimedean entire functions in any characteristic. In the positive characteristic case we prove more: the ring of rational integers is…

We introduce a Cherednik kernel and a hypergeometric function for integral root systems and prove their relation to spherical functions associated with Riemannian symmetric spaces of reductive Lie groups. Furthermore, we characterize the…

The exponential kernel \[E{g}(\lambda,w) = \exp -\frac{1}{\pi}\int_{\mathbb{C} } \frac{g(u)}{\overline{u-w} (u-\lambda) } da(u ),\] where the compactly supported bounded measurable function $g$ satisfies $0 \leq g\leq 1,$ and suitably…

The theory of Toeplitz quantization presented in our previous paper is extended and further developed to include diverse and interesting non-commutative realizations of the classical Euclidean plane. This is done using Hilbert spaces of…

Nevanlinna's five-value theorem is well-known as a famous theorem in value distribution theory, which asserts that two non-constant meromorphic functions on $\mathbb C$ are identical if they share five distinct values ignoring…

We present a systematic study of the family of positive definite (p.d.) kernels with the use of their associated feature maps and feature spaces. For a fixed set $X$, generalizing Loewner, we make precise the corresponding partially ordered…

We study several aspects concerning slice regular functions mapping the quaternionic open unit ball into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive…

This article investigates $k$-regular factorizations of characteristic functions associated with completely non-coisometric row contractions. In this setting, a one-to-one correspondence is established between chains of joint invariant…

We study reproducing kernel Hilbert spaces introduced as ranges of generalized Ces\`aro-Hardy operators, in one real variable and in one complex variable. Such spaces can be seen as formed by absolutely continuous functions on the positive…

The character of the exceptional series of representations of SU(1,1) is determined by using Bargmann's realization of the representation in the Hilbert space $H_\sigma$ of functions defined on the unit circle. The construction of the…

In his Annals of Mathematics paper (2009), Berndtsson proves an important result on the Nakano positivity of holomorphic infinite-rank vector bundles whose fibers are Hilbert spaces consisting of holomorphic $L^2$-functions with respect to…

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…

By making a seminal use of the maximum modulus principle of holomorphic functions we prove existence of $n$-best kernel approximation for a wide class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc, and for…

Henkin functionals on non-commutative $\mathrm{C}^*$-algebras have recently emerged as a pivotal link between operator theory and complex function theory in several variables. Our aim in this paper is characterize these functionals through…

We study properties of positive operators on Gelfand-Shilov spaces, and distributions which are positive with respect to non-commutative convolutions. We prove that boundedness of kernels $K \in \maclD_s^{\prime}$ to positive operators, are…

This survey shows how, for the Nevanlinna class N of the unit disc, one can define and often characterize the analogues of well-known objects and properties related to the algebra of bounded analytic functions $ H^\infty$: interpolating…

We give several characterizations of those finite dimensional HSRK with complete Pick kernels which are model spaces. One characterization involves the size of the solution to a multiplier problem. Another involves having a conjugation…

This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…

This article studies the problem of approximating functions belonging to a Hilbert space $\mathcal H_d$ with a reproducing kernel of the form $$\tilde K_d(\boldsymbol x,\boldsymbol t):=\prod_{\ell=1}^d…

We prove that the Bergman kernel function associated to a finitely connected domain in the plane is given as a rational combination of only three basic functions of one complex variable: an Alhfors map, its derivative, and one other…