Related papers: Multiresolution analysis on spectra of hermitian m…

We study invariant random matrix ensembles \begin{equation*} \mathbb{P}_n(d M)=Z_n^{-1}\exp(-n\,tr(V(M)))\,d M \end{equation*} defined on complex Hermitian matrices $M$ of size $n\times n$, where $V$ is real analytic such that the…

Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…

A very general class of resolved versions of the C/Z_N, T^2/Z_N and S^1/Z_2 orbifolds is considered and the free theory of 6D chiral fermions studied on it. As the orbifold limit is taken, localized 4D chiral massless fermions are seen to…

We study a class of scalar, linear, non-local Riemann-Hilbert problems (RHP) involving finite subgroups of PSL(2,C). We associate to such problems a (maybe infinite) root system and describe the relevance of the orbits of the Weyl group in…

For a Reproducing Kernel Hilbert Space on a complex domain we give a formula that describes the Hermitean metrics on the domain which are pull-backs of some metric on the (dual of) the RKHS via the evaluation map. Then we consider the…

We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of…

We develop an algebraic approach for finding the eigenfunctions of a large class of few and many-body Hamiltonians, in one and higher dimensions, having linear spectra. The method presented enables one to exactly map these interacting…

We give a definition of Radon hypergeometric function (Radon HGF) of confluent and nonconfluent type, which is a function on the Grassmannian Gr(m,nr) obtained as a Radon transform of a character of the universal covering group of…

Let $X$ be a Hermitian complex space of pure dimension $n$ with isolated singularities. In the present paper, we give a natural resolution for the canonical sheaf of square-integrable holomorphic $n$-forms with Dirichlet boundary condition…

We present an application-oriented approach to Urysohn and Hammerstein integral operators acting between spaces of H"older continuous functions over compact metric spaces. These nonlinear mappings are formulated by means of an abstract…

Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…

We study ambiguities in the precise formulation of the Wheeler-DeWitt equation for the wavefunction of the Universe that arise due to different operator orderings in the quantum Hamiltonian. We first examine the simpler case of the…

We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…

For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general…

We present an approach to sums of random Hermitian matrices via the theory of spherical functions for the Gelfand pair $(\mathrm{U}(n) \ltimes \mathrm{Herm}(n), \mathrm{U}(n))$. It is inspired by a similar approach of Kieburg and K\"osters…

We show continuity of solutions $u \in W^{1,n}(B^n,\mathbb{R}^N)$ to the system \[ -{\rm div} (|\nabla u|^{n-2} \nabla u) = \Omega \cdot |\nabla u|^{n-2} \nabla u \] when $\Omega$ is an $L^n$-antisymmetric potential -- and additionally…

We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…

. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of…

We study a system of $n$ Abelian vector fields coupled to $\frac 12 n(n+1)$ complex scalars parametrising the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. This model is Weyl invariant and possesses the maximal…

Starting from a generalization of Weyl's relations in finite dimension $N$, we show that the Heisenberg commutation relations can be satisfied in a specific $N-1$ dimensional subspace, and display a linear map for projecting operators to…