906 research outputs found
Irreducible Tensor Operators and the Wigner-Eckart Theorem for Finite Magnetic Groups
The transformation properties of irreducible tensor operators and the
applicability of the Wigner-Eckart theorem to finite magnetic groups have been
studied.Comment: 9 pages, 0 figure
Function with its Fourier transform supported on annulus and eigenfunction of Laplacian
We explore the possibilities of reaching the characterization of
eigenfunction of Laplacian as a degenerate case of the inverse Paley-Wiener
theorem (characterizing functions whose Fourier transform is supported on a
compact annulus) for the Riemannian symmetric spaces of noncompact type. Most
distinguished prototypes of these spaces are the hyperbolic spaces. The
statement and the proof of the main result work mutatis-mutandis for a number
of spaces including Euclidean spaces and Damek-Ricci spaces.Comment: 24 page
On the Schwartz space isomorphism theorem for rank one symmetric space
In this paper we give a simpler proof of the -Schwartz space isomorphism
under the Fourier transform for the class of functions of left
-type on a Riemannian symmetric space of rank one. Our treatment rests
on Anker's \cite{A} proof of the corresponding result in the case of left
-invariant functions on . Thus we give a proof which relies only on the
Paley--Wiener theorem.Comment: 16 page
Beurling's Theorem and Morgan's Theorem for Step Two Nilpotent Lie Groups
We prove Beurling's theorem and Morgan's theorem for step two
nilpotent Lie groupsComment: 20 page
Beurling's Theorem and characterization of heat kernel for Riemannian Symmetric spaces of noncompact type
We prove Beurling's theorem for rank 1 Riemmanian symmetric spaces and relate
it to the characterization of the heat kernel of the symmetric space
Asymptotic mean value property for eigenfunctions of the Laplace-Beltrami operator on Damek-Ricci spaces
Let be a Damek-Ricci space equipped with the Laplace-Beltrami operator
. In this paper we characterize all eigenfunctions of through
sphere, ball and shell averages as the radius (of sphere, ball or shell) tends
to infinity
Beurling's Theorem for
We prove Beurling's theorem for the full group . This is the {\em
master theorem} in the quantitative uncertainty principle as all the other
theorems of this genre follow from it
Chaotic behaviour of the Fourier multipliers on Riemannian symmetric spaces of noncompact type
Let be a Riemannian symmetric space of noncompact type and be a
linear translation-invariant operator which is bounded on . We shall
show that if is not a constant multiple of identity then there exist
complex constants such that is chaotic on when is in the
sharp range . This vastly generalizes the result that dynamics of
the (perturbed) heat semigroup is chaotic on proved in [15, 17].Comment: 17 page
Cowling-Price theorem and characterization of heat kernel on symmetric spaces
We extend the uncertainty principle, the Cowling--Price theorem, on
non-compact Riemannian symmetric spaces . We establish a characterization of
the heat kernel of the Laplace--Beltrami operator on from integral
estimates of the Cowling--Price type.Comment: 22 pages, no figures, no table
A note on growth of Fourier transforms and Moduli of continuity on Damek Ricci spaces
We obtain results related to boundedness of the growth of Fourier transform
by the modulus of continuity on Damek-Ricci spaces. For noncompact riemannian
symmetric spaces of rank one, analogues of all the results follow the same way
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