Results 11 to 20 of about 553 (167)

Bounds on Riesz Means of the Eigenvalues for Baouendi–Grushin Type Operators

International Journal of Mathematics and Mathematical Sciences
The aim of this paper is to consider spectral inequalities of a class of Baouendi–Grushin type operators in cylinders. Such operators are hypoelliptic and we obtain non-Weyl type inequalities depending on the rate of the degeneracy.
Alaa Aljahili, Ari Laptev
doaj   +2 more sources

Global Hölder Estimates via Morrey Norms for Hypoelliptic Operators with Drift [PDF]

Journal of Function Spaces, 2017
Suppose that X0,X1,…,Xm are left invariant real vector fields on the homogeneous group G with X0 being homogeneous of degree two and X1,…,Xm homogeneous of degree one.
Yuexia Hou, Pengcheng Niu
doaj   +2 more sources

Some Properties of Solutions to Weakly Hypoelliptic Equations [PDF]

International Journal of Differential Equations, 2013
A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size.
Christian Bär
doaj   +2 more sources

Index theorem for inhomogeneous hypoelliptic differential operators [PDF]

, 2023
We prove an index theorem for inhomogeneous differential operators satisfying the Rockland condition (hence hypoelliptic). This theorem extends an index theorem for contact manifolds by van Erp [48, 49]
Mohsen, O. (Omar)
core   +1 more source

Enhanced dissipation and Taylor dispersion in higher‐dimensional parallel shear flows

Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1358-1392, October 2023., 2023
Abstract We consider the evolution of a passive scalar advected by a parallel shear flow in an infinite cylinder with bounded cross section, in arbitrary space dimension. The essential parameters of the problem are the molecular diffusivity ν$\nu$, which is assumed to be small, and the wave number k$k$ in the streamwise direction, which can take ...
Michele Coti Zelati, Thierry Gallay
wiley   +1 more source

Lp-spectrum of degenerate hypoelliptic Ornstein-Uhlenbeck operators [PDF]

, 2021
We describe the spectrum of degenerate hypoelliptic Ornstein-Uhlenbeck operators A=∑i,j=1nqijDij+∑i,j=1nbijxjDi in Lp(Rn), 1 ...
Pallara D., Fornaro S., Schnaubelt R., Metafune G.   +3 more
core   +1 more source

Time regularity for generalized Mehler semigroups

Mathematische Nachrichten, Volume 295, Issue 11, Page 2223-2245, November 2022., 2022
Abstract We study continuity and Hölder continuity of t↦Ptf$t\mapsto P_tf$, where Pt$P_t$ is a generalized Mehler semigroup in Cb(X)$C_b(X)$, the space of the continuous and bounded functions from a Banach space X to R$\mathbb {R}$, and f∈Cb(X)$f\in C_b(X)$.
Alessandra Lunardi
wiley   +1 more source

Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models

Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 84, Issue 4, Page 1229-1256, September 2022., 2022
Abstract Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology—borrowing ideas from statistical physics and computational chemistry—for ...
Matthew M. Graham, Alexandre H. Thiery, Alexandros Beskos   +2 more
wiley   +1 more source

Analytic hypoellipticity of Keldysh operators

Proceedings of the London Mathematical Society, Volume 123, Issue 5, Page 498-516, November 2021., 2021
Abstract We consider Keldysh‐type operators, P=x1Dx12+a(x)Dx1+Q(x,Dx′), x=(x1,x′) with analytic coefficients, and with Q(x,Dx′) second order, principally real and elliptic in Dx′ for x near zero. We show that if Pu=f, u∈C∞, and f is analytic in a neighbourhood of 0, then u is analytic in a neighbourhood of 0.
Jeffrey Galkowski, Maciej Zworski
wiley   +1 more source

Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
The main aim of this survey article is to present several known results about vector‐valued almost periodic functions and their applications. We separately consider almost periodic functions depending on one real variable and almost periodic functions depending on two or more real variables.
Wei-Shih Du, Marko Kostić, Manuel Pinto, Antonio Masiello   +3 more
wiley   +1 more source