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On operators satisfying the Rockland condition

Waldemar Hebisch (1998)

Studia Mathematica

Let G be a homogeneous Lie group. We prove that for every closed, homogeneous subset Γ of G* which is invariant under the coadjoint action, there exists a regular kernel P such that P goes to 0 in any representation from Γ and P satisfies the Rockland condition outside Γ. We prove a subelliptic estimate as an application.

On parabolic Whittaker functions II

Sergey Oblezin (2012)

Open Mathematics

We propose a Givental-type stationary phase integral representation for the restricted Grm,N-Whittaker function, which is expected to describe the (S 1×U N)-equivariant Gromov-Witten invariants of the Grassmann variety Grm,N. Our key tool is a generalization of the Whittaker model for principal series U(gl N)-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van...

On positive Rockland operators

Pascal Auscher, A. ter Elst, Derek Robinson (1994)

Colloquium Mathematicae

Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on L p ( G ; d g ) . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on L 2 we prove that it is closed on each of the L p -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the L p -spaces, p ∈ [1,∞]. Further extensions...

On pseudocompact topological Brandt λ 0 -extensions of semitopological monoids

Oleg Gutik, Kateryna Pavlyk (2013)

Topological Algebra and its Applications

In the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category...

Currently displaying 2101 – 2120 of 3843