Related papers: Analytic operator-valued generalized Feynman integ…

We prove a Feynman path integral formula for the unitary group $ \exp(-itL_{v,\theta})$, $t\geq 0$, associated with a discrete magnetic Schr\"odinger operator $L_{v,\theta}$ on a large class of weighted infinite graphs. As a consequence, we…

We study the boundedness and compactness properties of the generalized integration operator $T_{g,a}$ when it acts between distinct Hardy spaces in the unit disc of the complex plane. This operator has been introduced by the first author in…

This article, addressed to a general audience of functional analysts, is intended to be an illustration of a few basic principles from `noncommutative functional analysis', more specifically the new field of {\em operator spaces.} In our…

This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat…

Partition- and moment functions for a general (not necessarily Gaussian) functional measure that is perturbed by a Gibbs factor are calculated using generalized Feynman graphs. From the graphical calculus, a new notion of Wick ordering…

This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a…

A "Bochner-type" integral for vector lattice-valued functions with respect to (possibly infinite) vector lattice-valued measures is presented with respect to abstract convergences, satisfying suitable axioms, and some fundamental properties…

Yangian-type differential operators are shown to constrain Feynman integrals beyond the restriction to integrable graphs. In particular, we prove that all position-space Feynman diagrams at tree level feature a Yangian level-one momentum…

For weighted Toeplitz operators $\T^N_\phi$ defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions $f$ to the integral equation $\T^N_\phi(f)=h$ in terms of the regularity of the symbol…

In this paper, the boundedness and compactness of generalized integration operators $T_g^{n,k}$ between different analytic tent spaces in the unit disc are completely characterized.

Let $({\mathcal X},d,\mu)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, the authors establish some equivalent characterizations for the boundedness of fractional…

In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of…

In this article, we investigate some standard geometric properties of the integral operators $$ J_\alpha [f](z)= \int_{0}^{z}\bigg(\frac{f(w)}{w}\bigg)^\alpha dw, \,\,\, \alpha \in \mathbb{C} \text{ and } |z|<1, $$ and $$ I_\beta [g](z)=…

Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…

Let $T=\mathbb R^d$. Let a function $Q:T^2\to\mathbb C$ satisfy $Q(s,t)=\bar{Q(t,s)}$ and $|Q(s,t)|=1$. A generalized statistics is described by creation operators $\partial_t^\dag$ and annihilation operators $\partial_t$, $t\in T$, which…

We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated…

We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \mathcal{H}_{k,l}=(-\Delta)^{l}+V(x), \] where $V$ is a…

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…

In 1958, Helson and Lowdenslager extended the theory of analytic functions to a general class of groups with ordered duals. In this context, analytic functions on such a group $G$ are defined as the integrable functions whose Fourier…

We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…