Differential calculus on path and loop spaces. II: Irreducibility of Dirichlet forms on loop spaces

DOI10.1016/S0007-4497(99)80007-4zbMath0937.60050WikidataQ127372976 ScholiaQ127372976MaRDI QIDQ1275922

Shigeki Aida

Publication date: 28 May 2000

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

zbMATH Keywords

Dirichlet formsloop spacesirreducibility of symmetric diffusion

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)

Related Items (14)

Martingale representation and logarithmic-Sobolev inequality for the fractional Ornstein-Uhlenbeck measure ⋮ On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold ⋮ On integration by parts formula and characterization of fractional Ornstein-Uhlenbeck process ⋮ Absence of spectral gaps on a class of loop spaces ⋮ Local spectral gaps on loop spaces. ⋮ Unnamed Item ⋮ A concrete estimate for the weak Poincaré inequality on loop space ⋮ Weak Poincaré inequalities on domains defined by Brownian rough paths ⋮ An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups ⋮ Poincaré inequality for weighted first order Sobolev spaces on loop spaces ⋮ A Poincaré inequality on loop spaces ⋮ Uniform positivity improving property, Sobolev inequalities, and spectral gaps ⋮ Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces ⋮ Stochastic Cohomology of the Frame Bundle of the Loop Space

Cites Work

• Equations différentielles sur l'espace de Wiener et formules de Cameron- Martin non-linéaires
• Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces
• Integration on loop groups. I: Quasi invariant measures
• Large deviations and the Malliavin calculus
• Lectures on stochastic differential equations and Malliavin calculus
• Orbital theory for affine Lie algebras
• Analysis on Wiener spaces. I: Nonlinear maps
• The geometry of loop groups
• Logarithmic Sobolev inequalities on loop groups
• Analysis on Wiener spaces. II: Differential forms
• Integration on loop groups. II: Heat equation for the Wiener measure
• Integration on loop groups. III: Asymptotic Peter-Weyl orthogonality
• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
• On the Ornstein-Uhlenbeck operators on Wiener-Riemannian manifolds
• Sobolev spaces of Banach-valued functions associated with a Markov process
• Sobolev spaces over loop groups
• Stochastic anticipative integrals on a Riemannian manifold
• Quasi sure analysis of stochastic flows and Banach space valued smooth functionals on the Wiener space
• Certain gradient flows and submanifolds in Wiener spaces
• Uniqueness of ground states for Schrödinger operators over loop groups
• Existence and uniqueness of physical ground states
• Gradient Estimates of Harmonic Functions and the Asymptotics of Spectral Gaps on Path Spaces.
• A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold
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