Related papers: Quantitatively Hyper-Positive Real Functions
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
This article carries out a qualitative analysis on a system of integral equations of the Hardy--Sobolev type. Namely, results concerning Liouville type properties and the fast and slow decay rates of positive solutions for the system are…
We introduce a condition on accretive matrix functions, called $p$-ellipticity, and discuss its applications to the $L^p$ theory of elliptic PDE with complex coefficients. Our examples are: (i) generalized convexity of power functions…
By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
Let $f$ be a positive multiplicative function and let $k\geq 2$ be an integer. We prove that if the prime values $f(p)$ converge to $1$ sufficiently slowly as $p\rightarrow +\infty$, in the sense that $\sum_{p}|f(p)-1|=\infty$, there exists…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…
Using the combinatorics of $\alpha$-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that…
Positive definite functions are fundamental to many areas of applied mathematics, probability theory, spatial statistics and machine learning, amogst others. Motivated by a problem coming from the maximum likelihood estimation under fixed…
In this paper we deal with composite rational functions having zeros and poles forming consecutive elements of an arithmetic progression. We also correct a result published earlier related to composite rational functions having a fixed…
We present certain existence criteria and parameterisations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as…
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
We introduce a new hierarchy over monotone set functions, that we refer to as $\mathcal{MPH}$ (Maximum over Positive Hypergraphs). Levels of the hierarchy correspond to the degree of complementarity in a given function. The highest level of…
We obtain new types of exponential decay laws for solutions of density-matrix master equations in the weak-coupling limit: after comparing with results already present in the literature and developing the necessary techniques, we study the…