## 200 Citations

### On polynomial structures over spheres

- Mathematics
- 2022

. We exhibit a link between the following a priori unrelated three problems: • In algebraic geometry: the non-existence of polynomial mappings between spheres, • In dynamical systems: the ergodicity…

### Inverse problems and rigidity questions in billiard dynamics

- MathematicsErgodic Theory and Dynamical Systems
- 2021

Abstract A Birkhoff billiard is a system describing the inertial motion of a point mass inside a strictly convex planar domain, with elastic reflections at the boundary. The study of the associated…

### Isospectralization, or How to Hear Shape, Style, and Correspondence

- Mathematics2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
- 2019

This paper introduces a numerical procedure called isospectralization, consisting of deforming one shape to make its Laplacian spectrum match that of another, and exemplifies its applications in some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics.

### Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups

- MathematicsThe Annals of Probability
- 2019

In this paper, we start by showing that the intertwining relationship between two minimal Markov semigroups acting on Hilbert spaces implies that any recurrent extensions, in the sense of It\^o, of…

### Submitted to the Annals of Probability INTERTWINING , EXCURSION THEORY AND KREIN THEORY OF STRINGS FOR NON-SELF-ADJOINT MARKOV SEMIGROUPS By

- Mathematics
- 2018

In this paper, we start by showing that the intertwining relationship between two minimal Markov semigroups acting on Hilbert spaces implies that any recurrent extensions, in the sense of Itô, of…

### Explorations of Infinitesimal Inverse Spectral Geometry

- Mathematics
- 2013

Spectral geometry is a mathematical discipline that studies the relationship between the geometry of Riemannian manifolds and the spectra of natural differential operators defined on them. The…

### Transient response functions for graph structure addressable memory

- Computer Science52nd IEEE Conference on Decision and Control
- 2013

This paper uses the transient behavior of random walk over graphs to compare their spectral resolution and collects data from intrinsically parallel random walks to form a graph response function as an effective measure of graph similarity.

### Can one hear the spanning trees of a quantum graph?

- MathematicsLetters in Mathematical Physics
- 2023

Kirchhoff showed that the number of spanning trees of a graph is the spectral determinant of the combinatorial Laplacian divided by the number of vertices; we reframe this result in the quantum graph…

### CR embeddability of quotients of the Rossi sphere via spectral theory

- MathematicsInternational Journal of Mathematics
- 2022

We look at the action of finite subgroups of SU(2) on [Formula: see text], viewed as a CR manifold, both with the standard CR structure as the unit sphere in [Formula: see text] and with a perturbed…

### Ergodic decompositions of Dirichlet forms under order isomorphisms

- MathematicsJournal of Evolution Equations
- 2022

We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a…

## References

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- MathematicsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- 1988

Abstract From a knowledge of the eigenvalue spectrum of the Laplacian on a domain, one may extract information on the geometry and boundary conditions by analysing the asymptotic expansion of a…

### The spectrum of positive elliptic operators and periodic bicharacteristics

- Mathematics
- 1975

Let X be a compact boundaryless C ∞ manifold and let P be a positive elliptic self-adjoint pseudodifferential operator of order m>0 on X. For technical reasons we will assume that P operates on…

### Heat equation for a region in R2 with a polygonal boundary

- Mathematics
- 1988

Soit D un ensemble connexe ouvert borne dans R 2 a frontiere ∂D. Soit Δ le laplacien de Dirichlet pour D et on definit pour t positif Z(+)=trace (exp iΔ). On etudie le comportement de Z(t) dans le…

### Introduction to Fourier Analysis on Euclidean Spaces.

- Mathematics
- 1971

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action…

### Fourier Analysis: An Introduction

- Biology
- 2003

This book discusses Fourier Analysis, Dirichlet's Theorem, and some Applications of Fourier Series 100 with a focus on the Fourier Transform.

### Eigenvalues and Eigenfunctions of the Laplacian 24 2 The Eigenvalue Problem 2 . 1 The eigenvalue equation

- Mathematics
- 2011

The problem of determining the eigenvalues and eigenvectors for linear operators acting on finite dimensional vector spaces is a problem known to every student of linear algebra. This problem has a…