Holomorphic functions and subelliptic heat kernels over Lie groups

DOI10.4171/JEMS/171zbMath1193.32023WikidataQ115212478 ScholiaQ115212478MaRDI QIDQ843189

Leonard Gross, Bruce K. Driver, Laurent Saloff-Coste

Publication date: 29 September 2009

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=11&iss=5&rank=1

zbMATH Keywords

heat kerneluniversal enveloping algebrasubellipticTaylor mapcomplex groups

Mathematics Subject Classification ID

(L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Subelliptic equations (35H20) Heat kernels in several complex variables (32W30) Complex spaces (32C15)

Related Items (17)

Sub-Laplacians on sub-Riemannian manifolds ⋮ Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups ⋮ Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups ⋮ Growth of Taylor coefficients over complex homogeneous spaces ⋮ A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups ⋮ Integration by parts and quasi-invariance for the horizontal Wiener measure on foliated compact manifolds ⋮ A reaction-diffusion equation on stratified groups ⋮ Holomorphic functions and the Itô chaos ⋮ Generalized Fredholm properties for invariant pseudodifferential operators ⋮ Heat kernel estimates for the \({{\bar{\partial}}}\)-Neumann problem on \(G\)-manifolds ⋮ The large-\(N\) limit of the Segal-Bargmann transform on \(\mathbb U_N\) ⋮ Riesz potentials and nonlinear parabolic equations ⋮ The Taylor map on complex path groups ⋮ Dimension-independent estimates for heat operators and harmonic functions ⋮ The Segal-Bargmann transform on classical matrix Lie groups ⋮ On extension problem, trace Hardy and Hardy's inequalities for some fractional Laplacians ⋮ The complex-time Segal-Bargmann transform

Cites Work

• The Segal-Bargmann ``coherent state transform for compact Lie groups
• Dirichlet forms and symmetric Markov processes
• Holomorphic functions and the heat kernel measure on an infinite dimensional complex orthogonal group
• On the Kakutani-Itô-Segal-Gross and Segal-Bargmann-Hall isomorphisms
• Heat kernel analysis of Cameron-Martin subgroup for infinite dimensional groups
• Hypoelliptic second order differential equations
• On a Hilbert space of analytic functions and an associated integral transform part I
• Surjectivity of the Taylor map for complex nilpotent Lie groups
• Some Norms on Universal Enveloping Algebras
• Harmonic analysis with respect to heat kernel measure
• TAYLOR MAP ON GROUPS ASSOCIATED WITH A II₁-FACTOR
• Unitary ℐ-spherical representations for split 𝓅-adic 𝐄₆
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