Results 21 to 30 of about 46 (37)

Subadditivity of homogeneous norms on certain nilpotent Lie groups

, 1981
Let N be a Lie group with its Lie algebra generated by the leftinvariant vector fields Xi,.. . ,Xk on N. An explicit fundamental solution for the (hypoelliptic) operator L = Xx + ■ ■ ■ + Xk on N has been obtained for the Heisenberg group by Folland [1 ...
J. Cygan
semanticscholar   +1 more source

Remarks on global hypoellipticity

, 1973
We study differential operators D which commute with a fixed normal elliptic operator E on a compact manifold M. We use eigenfunction expansions relative to E to obtain simple conditions giving global hypoellipticity. These conditions are equivalent to D
Stephen J. Greenfield, N. Wallach
semanticscholar   +1 more source

Weakly amenable groups and the RNP for some Banach algebras related to the Fourier algebra

, 2013
It is shown that if G is a weakly amenable unimodular group then the Banach algebra Ap(G) = Ap ∩ L(G), where Ap(G) is the Figà-Talamanca–Herz Banach algebra of G, is a dual Banach space with the Radon–Nikodym property if 1 ≤ r ≤ max(p, p′). This does not
E. Granirer
semanticscholar   +1 more source

Remark on commutative approximate identities on homogeneous groups

, 1992
We give, using the functional calculus of Hulanicki [4], a construction of a commutative approximate identity on every homogeneous group. In [2] Folland and Stein asked, whether on every homogeneous group X there is a function q in the Schwartz class 9(X)
Jacek Dziubański
semanticscholar   +1 more source

A decomposition for certain real semisimple Lie groups

, 1975
For a class of real semisimple Lie groups, including those for which G and K have the same rank, Kostant introduced the decomposition G = KNnK, where Nq is a certain abelian subgroup of N, and conjectured that the Jacobian of the decomposition with ...
H. Michelson
semanticscholar   +1 more source

Convolution operators on groups and multiplier theorems for Hermite and Laguerre expansions

, 1988
Using harmonic analysis on nilpotent Lie groups the following theorem is proved. Let a sequence {an} be defined by a function K E CN(R+) such that sup,>0 >K() (A)AJ
J. Długosz
semanticscholar   +1 more source

A class of solvable non-homogeneous differential operators on the Heisenberg group

, 2001
In [8], we studied the problem of local solvability of complex coefficient second order left-invariant differential operators on the Heisenberg group Hn, whose principal parts are “positive combinations of generalized and degenerate generalized ...
D. Müller, Zhenqiu Zhang
semanticscholar   +1 more source

A tauberian group algebra

, 1973
Let G be the group of real matrices Lex 0 (xX y) = y I (x, .y E R). Every proper closed two-sided ideal of L'(G) is contained in a maximal modular two-sided ideal.
Peter R. Mueller-Roemer
semanticscholar   +1 more source

Central measures on semisimple Lie groups have essentially compact support

, 1972
In this paper it is shown that for a connected semisimple Lie group with no nontrivial compact quotient any finite central measure is a discrete measure concentrated on the center of the group.
D. Ragozin, L. Rothschild
semanticscholar   +1 more source

Singular integrals on nilpotent Lie groups

, 1975
Convolution operators Tf(x) = ff(xy )K(y) dy on a class of nilpotent Lie groups are shown to be bounded on L0, 1 < p < o, provided the Euclidean Fourier transform of K (with respect to a coordinate system in which the group multiplication is in a special
R. Strichartz
semanticscholar   +1 more source