scholarly journals Pseudodifferential calculus on a singular foliation

2011 ◽  
pp. 125-152 ◽  
Author(s):  
Iakovos Androulidakis ◽  
Georges Skandalis
Keyword(s):  
Singular Foliation ◽  
Pseudodifferential Calculus

Riemannian metrics and Laplacians for generalized smooth distributions

2019 ◽  
pp. 1-47
Author(s):  
Iakovos Androulidakis ◽  
Yuri Kordyukov
Keyword(s):  
Laplace Operator ◽  
Smooth Manifold ◽  
Riemannian Metrics ◽  
Riemannian Metric ◽  
Constant Rank ◽  
Singular Foliation ◽  
Pseudodifferential Calculus ◽  
Underlying Manifold

We show that any generalized smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying manifold is compact, we show that it is essentially self-adjoint. Viewing this Laplacian in the longitudinal pseudodifferential calculus of the smallest singular foliation which includes the distribution, we prove hypoellipticity.

scholarly journals The analytic index of elliptic pseudodifferential operators on a singular foliation

2011 ◽  
Vol 8 (3) ◽  
pp. 363-385 ◽  
Author(s):  
Iakovos Androulidakis ◽  
Georges Skandalis
Keyword(s):  
Elliptic Operator ◽  
Pseudodifferential Operators ◽  
Current Paper ◽  
Singular Foliation ◽  
Pseudodifferential Calculus ◽  
Analytic Index ◽  
Theory Element

AbstractIn previous papers ([1, 2]) we defined the C*-algebra and the longitudinal pseudodifferential calculus of any singular foliation (M,). In the current paper we construct the analytic index of an elliptic operator as a KK-theory element, and prove that this element can be obtained from an “adiabatic foliation” on M×ℝ, which we introduce here.

SINGULAR FOLIATION GENERATED BY AN ORBIT OF FAMILY OF VECTOR FIELDS

2021 ◽  
Vol 10 (4) ◽  
pp. 2141-2147
Author(s):  
X.F. Sharipov ◽  
B. Boymatov ◽  
N. Abriyev
Keyword(s):  
Dynamical Systems ◽  
Euclidean Space ◽  
Control Theory ◽  
Vector Fields ◽  
Singular Foliation ◽  
Completely Integrable ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Systems Control

Geometry of orbit is a subject of many investigations because it has important role in many branches of mathematics such as dynamical systems, control theory. In this paper it is studied geometry of orbits of conformal vector fields. It is shown that orbits of conformal vector fields are integral submanifolds of completely integrable distributions. Also for Euclidean space it is proven that if all orbits have the same dimension they are closed subsets.

scholarly journals On the inner automorphisms of a singular foliation

2018 ◽  
Vol 293 (1-2) ◽  
pp. 725-729 ◽  
Author(s):  
Alfonso Garmendia ◽  
Ori Yudilevich
Keyword(s):  
Singular Foliation ◽  
Inner Automorphisms

scholarly journals Singular Foliation C ∗ -Algebras

1988 ◽  
Vol 104 (4) ◽  
pp. 1197 ◽  
Author(s):  
Albert Jeu-Liang Sheu
Keyword(s):  
Singular Foliation ◽  
C Algebras

Méthode BKW formelle et spectre des molécules polyatomiques dans l'approximation de Born–Oppenheimer

2001 ◽  
Vol 79 (4) ◽  
pp. 757-771 ◽  
Author(s):  
B Messirdi ◽  
A Senoussaoui
Keyword(s):  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Pseudodifferential Calculus ◽  
Coulomb Type ◽  
Formal Version

We studied the spectrum of P = -h2Δx – Δy + V (x,y) on L2(IRx3n × IRy3p), when h tends to zero, n [Formula: see text] 2, p [Formula: see text] IN*, in the case where the potential V(x,y) is singular and of Coulomb type and the first eigenvalue of Q (x) = -Δy + V(x,y) on L (IRy3p) admits an unbounded well. Using a formal version of the h-pseudodifferential calculus on the regularized operator of P with adapted changes, we obtained WKB-type expansions of eigenvalues and associated eigenfunctions of P.

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