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Spectra for Gelfand pairs associated with the Heisenberg group

Chal Benson, Joe Jenkins, Gail Ratcliff, Tefera Worku (1996)

Colloquium Mathematicae

Let K be a closed Lie subgroup of the unitary group U(n) acting by automorphisms on the (2n+1)-dimensional Heisenberg group H n . We say that ( K , H n ) is a Gelfand pair when the set L K 1 ( H n ) of integrable K-invariant functions on H n is an abelian convolution algebra. In this case, the Gelfand space (or spectrum) for L K 1 ( H n ) can be identified with the set Δ ( K , H n ) of bounded K-spherical functions on H n . In this paper, we study the natural topology on Δ ( K , H n ) given by uniform convergence on compact subsets in H n . We show that Δ ( K , H n ) is a complete...

Spectral multipliers on metabelian groups.

Waldemar Hebisch (2000)

Revista Matemática Iberoamericana

Let G be a Lie group, Xj right invariant vector fields on G, which generate (as a Lie algebra) the Lie algebra of G,L = -Σ Xj2.(...) In this paper we consider L1(G) boundedness of F(L) for (some) metabelian G and a distinguished L on G. Of the main interest is that the group is of exponential growth, and possibly higher rank. Previously positive results about higher rank groups were only about Iwasawa type groups. Also, our groups may be unimodular, so it is the second positive result (after [13])...

Spectral synthesis in L²(G)

Jean Ludwig, Carine Molitor-Braun, Sanjoy Pusti (2015)

Colloquium Mathematicae

For locally compact, second countable, type I groups G, we characterize all closed (two-sided) translation invariant subspaces of L²(G). We establish a similar result for K-biinvariant L²-functions (K a fixed maximal compact subgroup) in the context of semisimple Lie groups.

Sub-Laplacian with drift in nilpotent Lie groups

Camillo Melzi (2003)

Colloquium Mathematicae

We consider the heat kernel ϕ t corresponding to the left invariant sub-Laplacian with drift term in the first commutator of the Lie algebra, on a nilpotent Lie group. We improve the results obtained by G. Alexopoulos in [1], [2] proving the “exact Gaussian factor” exp(-|g|²/4(1+ε)t) in the large time upper Gaussian estimate for ϕ t . We also obtain a large time lower Gaussian estimate for ϕ t .

Sub-Laplacians of holomorphic L p -type on exponential Lie groups

Detlef Müller (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this survey article, I shall give an overview on some recent developments concerning the L p -functional calculus for sub-Laplacians on exponential solvable Lie groups. In particular, I shall give an outline on some recent joint work with W. Hebisch and J. Ludwig on sub-Laplacians which are of holomorphic L p -type, in the sense that every L p -spectral multiplier for p ≠ 2 will be holomorphic in some domain.

Currently displaying 261 – 280 of 334