Related papers: Observables as functions: Antonymous functions
A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
In this paper we initiate the study of real operator monotonicity for functions of tuples of operators, which are multivariate structured maps with a functional calculus called free functions that preserve the order between real parts (or…
Let $M$ be a commutative homogeneous space of a compact Lie group $G$ and $A$ be a closed $G$-invariant subalgebra of the Banach algebra $C(M)$. A function algebra is called antisymmetric if it does not contain nonconstant real functions.…
Eigenfunctions of the Askey-Wilson second order $q$-difference operator for $0<q<1$ and $|q|=1$ are constructed as formal matrix coefficients of the principal series representation of the quantized universal enveloping algebra…
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
Carath\'eodory functions, i.e. functions analytic in the open upper half-plane and with a positive real part there, play an important role in operator theory, $1D$ system theory and in the study of de Branges-Rovnyak spaces. The Herglotz…
We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of…
In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M-function see the same singularities as the resolvent of a certain restriction $A_B$ of the maximal operator? We obtain results showing…
In this note we define L-functions of finite graphs and study the particular case of finite cycles in the spirit of a previous paper that studied spectral zeta functions of graphs. The main result is a suggestive equivalence between an…
We introduce an approach to compute the renormalisation group flow of relational observables in quantum gravity which evolve from their microscopic expressions towards the full quantum expectation value. This is achieved by using the…
Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$}, \end{align*} are named the alternating invariant functions. Examples of such functions…
It is shown that correlations of dichotomic functions can not conform to results from Quantum Mechanics. Also, it is seen that the assumptions attendant to optical tests of Bell's Inequalities actually are consistent with classical physics…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\colon \mathbb S^d\rightarrow \mathbb R$ into a sum of terms $f_{\boldsymbol u,\boldsymbol \xi}$. The index $\boldsymbol u$ is a…
We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological induction for quantum groups.
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…
We revisit miscellaneous linear differential operators mostly associated with lattice Green functions in arbitrary dimensions, but also Calabi-Yau operators and order-seven operators corresponding to exceptional differential Galois groups.…