Related papers: Fundamental solution for (Delta - lambda_z)^n on a…

The N=2 supersymmetric extension of the Schr\"odinger-Hamiltonian with 1/r-potential in d dimension is constructed. The system admits a supersymmetrized Laplace-Runge-Lenz vector which extends the rotational SO(d) symmetry to a hidden…

The notion of a $\Gamma $-symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group $\Gamma $ replaces the group $Z_2$. The case $\Gamma =\Z_k$ has also been studied, from the…

In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…

We investigate infinite-level Shimura varieties within the framework of analytic stacks of Clausen-Scholze, developing their smooth, completed, locally analytic, and de Rham realizations. We formulate a Grothendieck-Messing-Hodge-Tate…

We summarize recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $\Gamma \backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $\Gamma$) or…

Using Polyakov's functional integral approach with the Liouville action functional defined in \cite{ZT2} and \cite{LTT}, we formulate quantum Liouville theory on a compact Riemann surface X of genus g > 1. For the partition function <X> and…

We establish global existence and derive sharp pointwise decay estimates of solutions to cubic Dirac and Dirac-Klein-Gordon systems on a curved background, close to the Minkowski spacetime. By squaring the Dirac operator, we reduce the…

The aim of this paper is to study in details the regular holonomic $D-$module introduced in \cite{[B.19]} whose local solutions outside the polar hyper-surface $\{\Delta(\sigma).\sigma_k = 0 \}$ are given by the local system generated by…

An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a sum formula for the logdet in terms of the logdets of the ordinary…

By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct consequence of our main…

Let G/H be a hyperbolic space over R C or H, and let K be a maximal compact subgroup of G. Let D denote a certain explicit invariant differential operator, such that the non-cuspidal discrete series belong to the kernel of D. For any…

In this paper we study the spectrum of a fundamental differential operator on a Hilbert-P\'olya space. A number is an eigenvalue of this differential operator if and only if it is a nontrivial zero of the Riemann zeta function. An explicit…

An approximation Ansatz for the operator solution, $U(z',z)$, of a hyperbolic first-order pseudodifferential equation, $\d_z + a(z,x,D_x)$ with $\Re (a) \geq 0$, is constructed as the composition of global Fourier integral operators with…

Below we study a linear differential equation $\MM (v(z,\eta))=\eta^M{v(z,\eta)}$, where $\eta>0$ is a large spectral parameter and $\MM=\sum_{k=1}^{M}\rho_{k}(z)\frac{d^k}{dz^k},\; M\ge 2$ is a differential operator with polynomial…

In this paper, we analyze the solvability of the discrete nonlinear Schr\"odinger equation \begin{equation*} i\beta(\Delta_t+\nabla_t)\phi(t,k) +\gamma |\phi(t,k)|^2\phi(t,k) +\varepsilon \Delta_k^2\phi(t,k-1) = g(t,\phi(t,k)),…

Let $(\Sigma,g)$ be a compact Riemannian surface without boundary and $\lambda_1(\Sigma)$ be the first eigenvalue of the Laplace-Beltrami operator $\Delta_g$. Let $h$ be a positive smooth function on $\Sigma$. Define a functional…

Let $X$ be a compact Riemann surface of genus $g\geq 2$ equipped with flat conical metric $|\Omega|$, where $\Omega$ be a holomorphic quadratic differential on $X$ with $4g-4$ simple zeroes. Let $K$ be the canonical line bundle on $X$.…

Let g be a complex semisimple Lie algebra and let G' be the Langlands dual group. We give a description of the cohomology algebra of an arbitrary spherical Schubert variety in the loop Grassmannian for G' as a quotient of the form…

Consider a classical elliptic pseudodifferential operator $P$ on ${\Bbb R}^n$ of order $2a$ ($0<a<1)$ with even symbol. For example, $P=A(x,D)^a$ where $A(x,D)$ is a second-order strongly elliptic differential operator; the fractional…

The kernel of the $\mathbb{Z}_2^{n}$ Dirac-Dunkl operator is examined. The symmetry algebra $\mathcal{A}_{n}$ of the associated Dirac-Dunkl equation on $\mathbb{S}^{n-1}$ is determined and is seen to correspond to a higher rank…