Related papers: Holomorphic Extensions of Laplacians and Their Det…

Given a unitary representation of a Lie group $G$ on a Hilbert space $\mathcal{H}$, we develop the theory of $G$-invariant self-adjoint extensions of symmetric operators both using von Neumann's theorem and the theory of quadratic forms. We…

We study the regularized determinant of the Laplacian as a functional on the space of Mandelstam diagrams (noncompact translation surfaces glued from finite and semi-infinite cylinders). A Mandelstam diagram can be considered as a compact…

Let $G$ be the semidirect product $N \rtimes \mathbb{R}$, where $N$ is a stratified Lie group and $\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $\mathbb{R}$ can be lifted to $G$,…

We develop a holomorphic equivalence between on one hand the space of pairs (stable bundle, flat connection on the bundle) and the "sheaf of holomorphic connections" (the sheaf of splittings of the one-jet sequence) for the determinant…

Given a three dimensional pseudo-Einstein CR manifold $(M,T^{1,0}M,\theta)$, we establish an expression for the difference of determinants of the Paneitz type operators $A_{\theta}$, related to the problem of prescribing the $Q'$-curvature,…

Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…

This article provides a deeper study of the Riesz transform commutators associated with the Neumann Laplacian operator $\Delta_N$ on $\mathbb R^n$. Along the line of singular value estimates for Riesz transform commutators established by…

We consider the Hodge Laplacian $\Delta$ on the Heisenberg group $H_n$, endowed with a left-invariant and U(n)-invariant Riemannian metric. For $0\le k\le 2n+1$, let $\Delta_k$ denote the Hodge Laplacian restricted to $k$-forms. Our first…

We give an integral representaion of the zeta-reguralized determinant of Laplacians on three dimensional Heisenberg manifolds, and study a behaivior of the values when we deform the uniform discrete subgroups. Heiseberg manifolds are the…

{Let $N, k$ be positive integers with $k\geq 2$, and $\Omega \subset \mathbb{R}^{N}$ be a domain.} By the well-known properties of the Laplacian and the gradient, we have \[ \Delta(f\cdot g)(x)=g(x) \Delta f(x)+f(x) \Delta g(x)+2\langle…

Fix a number $g>1$, let $S$ be a close surface of genus $g$, and $Teich(S)$ be the Teichm\"uller space of $S$ endowed with the Weil-Petersson metric. In this paper we show that the Riemannian sectional curvature operator of $Teich(S)$ is…

We study regularized determinants of Laplacians acting on the space of Hilbert-Maass forms for the Hilbert modular group of a real quadratic field. We show that these determinants are described by Selberg type zeta functions introduced in…

The logarithmic Laplacian on the (whole) N-dimensional Euclidean space is defined as the first variation of the fractional Laplacian of order 2s at s=0 or, alternatively, as a singular Fourier integral operator with logarithmic symbol.…

Let A be a commutative Banach algebra such that uA = {0} for u $\in$ A \ {0} which possesses dense principal ideals. The purpose of the paper is to give a general framework to define F (--$\lambda$1$\Delta$T 1 ,. .. , --$\lambda$ k…

Let $G$ be a finitely generated Kleinian group and let $\Delta$ be an invariant collection of components in its region of discontinuity. The Teichm\"uller space $T(\Delta,G)$ supported in $\Delta$, is the space of equivalence classes of…

Let M be a surface with conical singularities, and consider a degenerating family of surfaces obtained from M by removing disks of smaller and smaller radius around a subset of the conical singularities. Such families arise naturally in the…

The functional determinant of Laplace-type operators on the 3-dimensional non-compact hyperbolic manifold with invariant fundamental domain of finite volume is computed by quadratures and making use of the related terms of the Selberg trace…

In this paper we introduce a new family of operator-valued distributions on Euclidian space acting by convolution on differential forms. It provides a natural generalization of the important Riesz distributions acting on functions, where…

Let $\Omega\subset{\mathbb R}^n$ be bounded with a smooth boundary $\Gamma$ and let $S$ be the symmetric operator in $L^2(\Omega)$ given by the minimal realization of a second order elliptic differential operator. We give a complete…

We construct a parametrix of a resolvent of elliptic differential operators acting on half-densities on manifolds with ends. The construction is carried out by introducing suitable pseudodifferential operators compatible with the end…