Related papers: Positive Populations
An intuitive probabilistic alternative for the construction of the Martin boundary is presented along with a construction of maximal representing measures for positive harmonic functions.
The problem to decide whether a given rational function in several variables is positive, in the sense that all its Taylor coefficients are positive, goes back to Szeg\H{o} as well as Askey and Gasper, who inspired more recent work. It is…
We study fixed points of iterates of dynamically affine maps (a generalisation of Latt\`es maps) over algebraically closed fields of positive characteristic $p$. We present and study certain hypotheses that imply a dichotomy for the…
Many well-known positive linear operators (like Bernstein, Baskakov, Sz\'{a}sz-Mirakjan) are constructed by using specific fundamental functions. The sums of the squared fundamental functions have been objects of study in some recent…
We construct "quantum theta bases," extending the set of quantum cluster monomials, for various versions of skew-symmetric quantum cluster algebras. These bases consist precisely of the indecomposable universally positive elements of the…
Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current…
In this paper we provide some quantitative one-sided estimates that recover the dependences in the classical setting. Among them we provide estimates for the one-sided maximal function in Lorentz spaces and we show that the conjugation…
In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
We begin a study of Schur analysis in the setting of the Grassmann algebra, when the latter is completed with respect to the $1$-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and…
Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended…
We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the…
We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their…
The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use successive approximation of solutions, ensuring its positivity. To…
We give a probabilistic interpretation of the Dedekind zeta functions of $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$ using zeta integrals and use this to show that the first two Li coefficients of these zeta functions are positive.…
It is proved that the Epstein zeta-function corresponding to a binary positive definite quadratic form with integer coefficients has a positive proportion of its non-trivial zeros on the critical line.
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
In this paper, we introduce the concepts of the $u$-bracket, finite multiple harmonic $u$-series, and $u$-multiple zeta values via the Carlitz module. These objects serve as function field counterparts to the classical theory of…
The recent theorem by D.Luecking about finite rank Bergman-Toeplitz operators is extended to weights being distributions with compact support and to the spaces of harmonic functions.
We describe several classes of holomorphic functions of positive real part on the unit ball; each is characterized by an operator-valued Herglotz formula. Motivated by results of J.E. McCarthy and M. Putinar, we define a family of weighted…