Related papers: On a spectral representation for correlation measu…

Let $G$ be a semi-direct product $G=A\times_\phi K$ with $A$ Abelian and $K$ compact. We characterize spread-out probability measures on $G$ that are mixing by convolutions by means of their Fourier transforms. A key tool is a spectral…

In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle H…

In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…

We propose a definition for a Tau function and a spinor kernel (closely related to Baker-Akhiezer functions), where times parametrize slow (of order 1/N) deformations of an algebraic plane curve. This definition consists of a formal…

A Borel probability measure $\mu$ on a locally compact group is called a spectral measure if there exists a subset of continuous group characters which forms an orthogonal basis of the Hilbert space $L^2(\mu)$. In this paper, we…

A connected homogeneous space X=G/K is called commutative if G is a connected Lie group, $K$ is a compact subgroup and the B*-algebra L^1(X)^K of K-invariant integrable function on X is commutative. In this article we introduce the space…

Let K be a compact Lie group, endowed with a bi-invariant Riemannian metric. The complexification G of K inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and left and right translation turn the…

In this paper we develop a rigorous foundation for the study of integration and measures on the space $\mathscr{G}(V)$ of all graphs defined on a countable labelled vertex set $V$. We first study several interrelated $\sigma$-algebras and a…

We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…

The "spectral correlation function" analysis we introduce in this paper is a new tool for analyzing spectral-line data cubes. Our initial tests, carried out on a suite of observed and simulated data cubes, indicate that the spectral…

Using projective spaces as examples of toric manifolds, we examine K-theoretic fixed point localization. On the one hand, we will see how the permutation-equivariant theory of the point target space emerges as a necessary ingredient. On the…

We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Naimark's dilation theorem is given. The same approach is used to describe the spectrum of all unitary…

After a brief review of the definition of the Trudinger-Moser functions in dimension $N=2$ and some basic notions in the theory of ``Reproducing Kernel Hilbert Spaces (RKHS)'', we will show that there is a close connection between those two…

The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…

Let $\vec{p}\in(0,1]^n$ be a $n$-dimensional vector and $A$ a dilation. Let $H_A^{\vec{p}}(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of…

The Singer algebraic transfer is a fundamental homomorphism in algebraic topology, providing a bridge between the homology of classifying spaces and the cohomology of the Steenrod algebra $\mathcal{A}$, which forms the $E_2$-term of the…

In this work we extend the Fourier-Stieltjes transform of a vector measure and a continuous function defined on compact groups to locally compact groups. To do so, we consider a representation L of a normal compact subgroup K of a locally…

Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This…

Under mild conditions, it is possible to obtain, from almost purely measure-theoretic considerations and without any specific reference to stochastic processes, a change-of-measures result, resembling the usual Radon-Nikod\'ym change of…

The purpose of this paper is to provide a both comprehensive and summarizing account on recent results about analysis and geometry on configuration spaces $\Gamma_X$ over Riemannian manifolds $X$. Particular emphasis is given to a complete…