arXiv research

Local corner-factor conjecture for Neumann jump determinants supported by models.

Generalizes results on Bieri-Neumann-Strebel-Renz invariants and tropical varieties.

The paper efficiently solves a complex option valuation equation for two assets.

Study connects boundary geometry to symbol of Dirichlet-to-Neumann operator.

Study on learnability of Schatten--von Neumann operators in learning theory.

We study differential operators on complete Riemannian manifolds which act on sections of a bundle of finite type modules over a von Neumann algebra with a trace. We prove a relative index and a Callias-type index theorems for von Neumann indexes of such operators. We apply these results to obtain a version of Atiyah's…

Abstract: Expresses zeta-determinant of Dirichlet-to-Neumann operator on forms.

The Dirichlet-to-Neumann map for differential forms on a Riemannian manifold with boundary is a generalization of the classical Dirichlet-to-Neumann map which arises in the problem of Electrical Impedance Tomography. We synthesize the two different approaches to defining this operator by giving an invariant definition …

Study reveals how boundary wave operator determines metric properties on anti-de Sitter spacetimes.

Solves Neumann problem on CR manifold boundary.

This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional time-homogeneous diffusions even for the cases where the corresponding transition den…

Paper derives a formula for the determinant of Dirichlet-to-Neumann operator on Riemann surfaces.

Abstract: Shows nonexistence of Courant-type nodal domain bounds for eigenfunctions of Dirichlet-to-Neumann operator.

We establish the existence of analytic curves of eigenvalues for the Laplace-Neumann operator through an analytic variation of the metric of a compact Riemannian manifold $M$ with boundary by means of a new approach rather than Kato's method for unbounded operators. We obtain an expression for the derivative of the cur…

Study sharp lower bounds on negative eigenvalues of magnetic Pauli operator.

For $1\leq q \leq n-2$, we provide explicit examples to demonstrate non-compactness of the Neumann operator for the Kohn Laplacian acting on $L^2$ $(0,q)$-forms on the unit ball in $(2n+1)$-dimensional Heisenberg space.

We provide criteria for self-adjointness and τ-Fredhomness of first and second order differential operators acting on sections of infinite dimensional bundles, whose fibers are modules of finite type over a von Neumann algebra A endowed with a trace τ. We extend the Callias-type index to operators acting on sections of…

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

We study the linearization of the Dirichlet-to-Neumann map for Poincaré-Einstein metrics in even dimensions on an arbitrary compact manifold with boundary. By fixing a suitable gauge, we make the linearized Einstein equation elliptic. In this gauge the linearization of the Dirichlet-to-Neumann map appears as the scatte…

We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula involves the scattering matrix over the manifold with cylindrical end. We also …

We compute the whole spectrum of the Dirichlet-to-Neumann operator acting on differential p-forms on the unit Euclidean ball. Then, we prove a new upper bound for its first eigenvalue on a domain $Ω$ in Euclidean space in terms of the isoperimetric ratio ${\rm Vol}(\bdΩ)/{\rm Vol}(Ω)$.

Study Dirichlet-to-Neumann maps on manifolds, focusing on covering and total spaces.

We relate the spectral flow to the index for paths of selfadjoint Breuer-Fredholm operators affiliated to a semifinite von Neumann algebra, generalizing results of Robbin-Salamon and Pushnitski. Then we prove the vanishing of the von Neumann spectral flow for the tangential signature operator of a foliated manifold whe…

Anisotropic metric on manifolds uniquely determined by boundary data.

Bounds and estimates for eigenvalues of poly-harmonic and biharmonic operators.

We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Steklov problem on functions. We derive a number of upper and lower bounds for the first eigenvalue in several contexts: many of thes…

A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed light on the relationship between the scattering construction of Graham-Zworski…

Study Cheeger inequalities for Riemannian manifolds with boundary.

Study shows continuity of non-orientable surface determination from Dirichlet-to-Neumann map.

Recent research connects Hörmander's old work to modern boundary Laplacian analysis.

In this paper we present a proof of a Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds. A key p oint is the simple geometric nature of the constant in the a priori estimate of this maximum principle. In particular, this maximum principle can be applied to manifolds with Ricci curv…

Introduces differential forms to study inequalities between eigenvalues.

This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is …

Making use of its smooth structure only, out of a connected oriented smooth $4$-manifold a von Neumann algebra is constructed. It is geometric in the sense that is generated by local operators and as a special four dimensional phenomenon it contains all algebraic (i.e., formal or coming from a metric) curvature tensors…

The paper shows connections can be uniquely determined by their boundary data.

Toeplitz operators linked to submultiplicative filtrations and weighted Bergman kernels.

Estimates eigenvalues and spectrum for graph substructures using isocapacitary constants.

} In this article, we put forward a Neumann eigenvalue problem for the bi-harmonic operator $Δ^2$ on a bounded smooth domain $\Om$ in the Euclidean $n$-space ${\bf R}^n$ ($n\ge2$) and then prove that the corresponding first non-zero eigenvalue $Υ_1(\Om)$ admits the isoperimetric inequality of Szegö-Weinberger type: $Υ_…

Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generaliz…

We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the…

Structural-Jump-LSTM speeds up reading by skipping and jumping text.

Dirichlet-Neumann duality for Riemannian submersions

New framework shows $C^*$-simplicity for groups without certain subalgebras.

Computes indices of mixed order Dirac-type operators and related tensor fields.

Study applies inverse scattering to BKM systems, linking spectra and integrable systems.

Paper generalizes kernel mean embedding to von Neumann-algebra-valued measures.

We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator $D_m$ on the maximal Connes-Skandalis Hilbert module and explain how the functional calculus of $D_m$ encodes both the leafwise calculus…

Paper bounds the A-hat genus using curvature and isoperimetric constants.