Related papers: Some remarks on Tr\`eves' conjecture

These notes cover the contents of three survey lectures held at the ICTP Trieste Summer school on High dimensional manifold theory 2001. They introduce techniques coming from the theory of operator algebras. We will focus on the basic…

We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…

We prove a conjecture of Morel identifying Voevodsky's homotopy invariant sheaves with transfers with spectra in the stable homotopy category which are concentrated in degree zero for the homotopy t-structure and have a trivial action of…

The concept of polytopes was a milestone in elementary integral group theory. In this article, we will extend the concept of contra-linearly stochastic lines to H-Positive Definite Monoids. We will show that by adding the Non-Gaussian…

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…

We introduce the notion of mixed trTLEP-structures and prove that a mixed trTLEP-structure with some conditions naturally induces a mixed Frobenius manifold. This is a generalization of the reconstruction theorem of Hertling and Manin. As a…

We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…

A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of finite-gap integration. The parametrisation of the solutions…

In this first part of the paper, we define a natural dual object for manifolds with corners and show how pseudodifferential calculus on such manifolds can be constructed in terms of the localization principle in C*-algebras. In the second…

We use Hodge-theoretic methods to (i) explain number-theoretic identities of a type recently considered by Guillera and Zudilin, (ii) describe the Frobenius dual of Abel-Jacobi period functions, and (iii) offer a new proof of Golyshev's…

We consider an operator $ P $ which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form $ \sigma $ is not constant on $ \Char P $.…

This paper is concerned at the minimization fundamental gap problem for a class of two-dimensional degenerate sub-elliptic operators. We establish existence results for weak solutions, Sobolev embedding theorem and spectral theory of…

Multidimensional hypoelliptic diffusions arise naturally in different fields, for example to model neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. In this paper we…

An approach to the construction of index formulas for elliptic operators on singular manifolds is suggested on the basis of K-theory of algebras and cyclic cohomology. The equivalence of Toeplitz and pseudodifferential quantizations, well…

We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…

We establish the existence of a bounded $H_\infty$-calculus for a large class of hypoelliptic pseudodifferential operators on R^n and closed manifolds.

The simplest and most natural examples of completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions are the nilpotent operators. The main purpose of this paper is to prove the…

We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is \Phi_{p,q}(A_1,A_2,...,A_m) = (trace((\sum_{j=1}^m A_j^p)^{q/p}))^{1/q} for m positive definite…

We describe the set of points of the trianguline variety over a given local Galois representation. Global analogues describing companion points in eigenvariety by [Bre14] and [HN17], can be thought of as a rational analogue to the weight…

We prove some existence results for a class of nonlinear fractional equations driven by a nonlocal operator.