arXiv research

Unified framework for solving fixed-point equations in deterministic and stochastic settings.

Unified analysis of stochastic iterative algorithms using Lyapunov functions.

New Q-learning method achieves optimal sample complexity for average-reward problems.

This paper completes the construction of arbitrary order conformally invariant differential operators in higher spin spaces. Jan Slovák has classified all conformally invariant differential operators on locally conformally flat manifolds. We complete his results in higher spin theory by giving explicit expressions for …

The paper connects eigenvalue problems for various operators and establishes inequalities and asymptotic formulas for heat traces.

Introduces a new elliptic operator with positive eigenvalue.

Proves Kato inequalities for various conformal operators.

We describe a set of conformally covariant boundary operators associated to the Paneitz operator, in the sense that they give rise to a conformally covariant energy functional for the Paneitz operator on a compact Riemannian manifold with boundary. These operators naturally give rise to a first- and third-order conform…

Study on biharmonic hypersurfaces with specific recurrent operators in Euclidean space.

Local index theorem for chiral geometric operators proved using heat kernel.

Study estimates eigenvalues for concave Hessian operators on convex domains.

The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.

GJMS operators connect geometry, analysis, and physics.

Extends Calabi operator to Riemannian locally symmetric spaces.

New spectral torsion defined for rescaled Dirac operators.

Proves formal self-adjointness of certain differential operators.

The paper proves new theorems about specific types of operator perturbations.

Study of Dirac-like operators on spin manifolds with large mass parameters.

Study essential spectrum of differential operators on geometrically finite orbifolds.

The study proves inequalities for complex operators on curved spaces.

Study on opers over complex manifolds of dimension one.

Mixtures of neural operators reduce active complexity in operator learning.

Formula for Hadamard coefficients from Green's operators on spacetimes.

Study perturbs Dirac operators in any dimension, focusing on Majorana fermions.

Identifies Lorentzian locally symmetric spaces where Calabi operator suffices to determine Killing operator range.

Researchers create a family of conformally covariant operators.

The paper revisits and analyzes the tmd-operator in almost Kähler manifolds.

The k-Dirac operator is a differential operator which is natural to geometric structure of a parabolic type. We will give a set of initial conditions for this operator. In the proof of the claim we will need to adapt some parts from the theory of exterior differential systems to the setting of weighted differential ope…

We describe a set of conformally covariant boundary operators associated to the sixth-order GJMS operator on a conformally invariant class of manifolds which includes compactifications of Poincaré--Einstein manifolds. This yields a conformally covariant energy functional for the sixth-order GJMS operator on such manifo…

The paper derives expansions for Green's operators and resolvents using Hadamard methods.

The paper quantizes Kähler manifolds using differential operators.

The paper classifies and proves properties of symmetry breaking operators for specific groups.

New operators generalize Michelsohn's on almost Hermitian manifolds.

Paper quantifies neural operators' efficiency for solving nonlinear parabolic PDEs.

Researchers describe local properties of Haantjes operators.

We use the spectra of Dirac type operators on the sphere $S^{n}$ to produce sharp $L^{2}$ inequalities on the sphere. These operators include the Dirac operator on $S^{n}$, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers o…

Paper introduces new fractional Dirac operator and Q-curvature.

GNPs learn operators on non-Euclidean geometries using neural networks.

Develops a framework for learning nonlinear operators using Mercer kernels.

Introduces a new operator generating higher Koszul brackets on differential forms.

We consider the operator algebra generated by pseudodifferential operators on a closed smooth surface and shift operator induced by a Morse--Smale diffeomorphism of this surface. Elements in this algebra are considered as operators in the scale of Sobolev spaces and the aim of this paper is to describe how Fredholm pro…

New braided Frobenius algebras created from specific Hopf algebras.

The paper provides formulas for Hadamard coefficients using Green's operators.

Green-hyperbolic operators are linear differential operators acting on sections of a vector bundle over a Lorentzian manifold which possess advanced and retarded Green's operators. The most prominent examples are wave operators and Dirac-type operators. This paper is devoted to a systematic study of this class of diffe…

Study magnetic Schrödinger operators in Euclidean space.

For CR structures in dimension three, the CR pluriharmonic functions are characterized by the vanishing of a third order operator. This third order operator, after composition with the divergence operator, gives the fourth order analogue of the Paneitz operator. In this short note, we give criteria under which the kern…

We construct continuously parametrised families of conformally invariant boundary operators on densities. These may also be viewed as conformally covariant boundary operators on functions and generalise to higher orders the first-order conformal Robin operator and an analogous third-order operator of Chang-Qing. Our fa…

We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions of families of such operators. In one direction, we show that any homogeneous conformally variational scalar Riemannian invariant (CVI) induces one of these operators. In another direction, we u…