Related papers: Invariant measures on the circle and functional eq…

In this paper, we study the properties of a certain class of Borel measures on $\mathbb{R}^n$ that arise in the integral representation of Herglotz-Nevanlinna functions. In particular, we find that restrictions to certain hyperplanes are of…

In this article, a characterization of the class of Herglotz-Nevanlinna functions in $n$ variables is given in terms of an integral representation. Furthermore, alternative conditions on the measure appearing in this representation are…

One way to interpret smoothness of a measure in infinite dimensions is quasi-invariance of the measure under a class of transformations. Usually such settings lack a reference measure such as the Lebesgue or Haar measure, and therefore we…

We study Gibbs measures invariant under the flow of the NLS on the unit disc of $\R^2$. For that purpose, we construct the dynamics on a phase space of limited Sobolev regularity and a wighted Wiener measure invariant by the NLS flow. The…

This survey shows how, for the Nevanlinna class N of the unit disc, one can define and often characterize the analogues of well-known objects and properties related to the algebra of bounded analytic functions $ H^\infty$: interpolating…

In this paper we provide universal formulas describing Drinfeld-type quantization of inhomogeneous orthogonal groups determined by a metric tensor of an arbitrary signature living in a spacetime of arbitrary dimension. The metric tensor…

Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…

In this paper we analyze the derivative nonlinear Schr\"odinger equation on $\mathbb{T}$ with randomized initial data in $\cap_{s < \frac{1}{2}} H^{s}(\mathbb{T})$ according to a Wiener measure. We construct an invariant measure at each…

A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…

In this note we continue the analysis of metric measure space with variable ricci curvature bounds. First, we study $(\kappa,N)$-convex functions on metric spaces where $\kappa$ is a lower semi-continuous function, and gradient flow curves…

In this paper we develop a theory of curvature (resp. multiplicity) invariant for tensor products of full Fock spaces and also for tensor products of symmetric Fock spaces. This is an attempt to find a more general framework for these…

We consider the real-valued defocusing modified Korteweg-de Vries equation (mKdV) on the circle. Based on the complete integrability of mKdV, Killip-Vi\c{s}an-Zhang (2018) discovered a conserved quantity which they used to prove low…

Let h be a real-analytic function in the neighborhood of some compact set K on the plane. We show that for any complex measure on the Euclidean space of a finite total variation without singular components with the Fourier--Stieltjes…

We investigate ergodic-theoretical quantities and large deviation properties of one-dimensional intermittent maps, that have not only an indifferent fixed point but also a singular structure such that the uniform measure is invariant under…

We derive an explicit expression for the Haar integral on the quantized algebra of regular functions C_q[K] on the compact real form K of an arbitrary simply connected complex simple algebraic group G. This is done in terms of the…

A complex function $f(z)$ is called a Herglotz-Nevanlinna function if it is holomorphic in the upper half-plane ${\mathbb C}_+$ and maps ${\mathbb C}_+$ into itself. By a maximum principle a Herglotz-Nevanlinna function which takes a real…

The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…

It is known, that every function on the unit sphere in $\bbr^n$, which is invariant under rotations about some coordinate axis, is completely determined by a function of one variable. Similar results, when invariance of a function reduces…

Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint…