scholarly journals Radon transform on affine buildings of rank three

1999 ◽  
Vol 66 (1) ◽  
pp. 66-89 ◽  
Author(s):  
Laura Atanasi
Keyword(s):  
Radon Transform ◽  
Finite Rank ◽  
Affine Buildings ◽  
Locally Finite ◽  
Inversion Formulas

AbstractWe define the Radon transform for functions on the set of chambers of affine, locally finite, rank three buildings. We investigate the problem of the inversion of this transform. Explicit inversion formulas are exhibited for functions which fulfill required summability conditions.

Locally Finite Groups with Centralizers of Finite Rank

2016 ◽  
Vol 44 (12) ◽  
pp. 5074-5087 ◽  
Author(s):  
Kıvanc̣ Ersoy ◽  
Chander Kanta Gupta
Keyword(s):  
Finite Groups ◽  
Finite Rank ◽  
Locally Finite ◽  
Locally Finite Groups

Cartan Subalgebras of

2003 ◽  
Vol 46 (4) ◽  
pp. 597-616 ◽  
Author(s):  
Karl-Hermann Neeb ◽  
Ivan Penkov
Keyword(s):  
Finite Rank ◽  
Characteristic Zero ◽  
Cartan Subalgebra ◽  
Adjoint Representation ◽  
Linear Functionals ◽  
Maximal Subalgebra ◽  
Locally Finite ◽  
One Dimensional ◽  
Cartan Subalgebras ◽  
Locally Nilpotent

AbstractLet V be a vector space over a field of characteristic zero and V* be a space of linear functionals on V which separate the points of V. We consider V ⊗ V* as a Lie algebra of finite rank operators on V, and set (V, V*) := V ⊗ V*. We define a Cartan subalgebra of (V, V*) as the centralizer of a maximal subalgebra every element of which is semisimple, and then give the following description of all Cartan subalgebras of (V;V*) under the assumption that is algebraically closed. A subalgebra of (V, V*) is a Cartan subalgebra if and only if it equals for some one-dimensional subspaces Vj ⊆ V and (Vj)* ⊆ V* with (Vi)* (Vj) = δij and such that the spaces . We then discuss explicit constructions of subspaces Vj and (Vj)* as above. Our second main result claims that a Cartan subalgebra of (V, V*) can be described alternatively as a locally nilpotent self-normalizing subalgebra whose adjoint representation is locally finite, or as a subalgebra h which coincides with the maximal locally nilpotent h-submodule of (V, V*), and such that the adjoint representation of is locally finite.

METHOD OF MEAN VALUE OPERATORS FOR RADON TRANSFORMS IN THE SPACE OF MATRICES

2008 ◽  
Vol 19 (03) ◽  
pp. 245-283 ◽  
Author(s):  
E. OURNYCHEVA ◽  
B. RUBIN
Keyword(s):  
Radon Transform ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Necessary And Sufficient Conditions ◽  
Inversion Method ◽  
Radon Transforms ◽  
Inversion Formulas ◽  
Higher Rank ◽  
Necessary And Sufficient

We extend the Funk–Radon–Helgason inversion method of mean value operators to the Radon transform [Formula: see text] of continuous and Lpfunctions which are integrated over matrix planes in the space of real rectangular matrices. Necessary and sufficient conditions of existence of [Formula: see text] for such f and explicit inversion formulas are obtained. New higher-rank phenomena related to this setting are investigated.

The vertical slice transform on the unit sphere

2019 ◽  
Vol 22 (4) ◽  
pp. 899-917 ◽  
Author(s):  
Boris Rubin
Keyword(s):  
Unit Sphere ◽  
Radon Transform ◽  
Integral Geometry ◽  
Singular Value ◽  
Hypersingular Integrals ◽  
Inversion Formulas ◽  
Spherical Mean ◽  
Singular Value Decompositions ◽  
Vertical Slice ◽  
Class Of Functions

Abstract The vertical slice transform in spherical integral geometry takes a function on the unit sphere Sn to integrals of that function over spherical slices parallel to the last coordinate axis. This transform was investigated for n = 2 in connection with inverse problems of spherical tomography. The present article gives a survey of some methods which were originally developed for the Radon transform, hypersingular integrals, and the spherical mean Radon-like transforms, and can be adapted to obtain new inversion formulas and singular value decompositions for the vertical slice transform in the general case n ≥ 2 for a large class of functions.

scholarly journals Spectra of conjugated ideals in group algebras of abelian groups of finite rank and control theorems

1996 ◽  
Vol 38 (3) ◽  
pp. 309-320 ◽  
Author(s):  
Anatolii V. Tushev
Keyword(s):  
Finite Rank ◽  
Torsion Group ◽  
Group Algebras ◽  
Prime Ideals ◽  
Locally Finite ◽  
Torsion Free Group ◽  
Free Rank ◽  
And Control ◽  
Torsion Free Rank ◽  
Torsion Free

Throughout kwill denote a field. If a group Γ acts on aset A we say an element is Γ-orbital if its orbit is finite and write ΔΓ(A) for the subset of such elements. Let I be anideal of a group algebra kA; we denote by I+ the normal subgrou(I+1)∩A of A. A subgroup B of an abelian torsion-free group A is said to be dense in A if A/B is a torsion-group. Let I be an ideal of a commutative ring K; then the spectrum Sp(I) of I is the set of all prime ideals P of K such that I≤P. If R is a ring, M is an R-module and x ɛ M we denote by the annihilator of x in R. We recall that a group Γ is said to have finite torsion-free rank if it has a finite series in which each factoris either infinite cyclic or locally finite; its torsion-free rank r0(Γ) is then defined to be the number of infinite cyclic factors in such a series.

ENDOMORPHISMS OF DISCRETE GROUPS ACTING CHAMBER TRANSITIVELY ON AFFINE BUILDINGS

1993 ◽  
Vol 03 (03) ◽  
pp. 357-364 ◽  
Author(s):  
JOHN MEIER
Keyword(s):  
Coxeter Groups ◽  
Type A ◽  
Discrete Groups ◽  
Affine Buildings ◽  
Locally Finite ◽  
Finite Affine ◽  
Affine Building

Let Γ be a group acting chamber transitively by type preserving automorphisms on a locally finite affine building of type Ã2. We show that Out(Γ) is finite and that Γ is Hopfian. We apply our results to affine Coxeter groups and a family of four groups discovered by J. Tits.

scholarly journals On Radon transforms between lines and hyperplanes

2017 ◽  
Vol 28 (13) ◽  
pp. 1750093 ◽  
Author(s):  
Boris Rubin ◽  
Yingzhan Wang
Keyword(s):  
Radon Transform ◽  
Symmetric Case ◽  
Fractional Integrals ◽  
Radon Transforms ◽  
Full Generality ◽  
Inversion Formulas ◽  
Radial Functions ◽  
Kelvin Transform ◽  
Funk Transform ◽  
Dual Transform

We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in [Formula: see text]. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions that are constant on symmetric clusters of lines. For the corresponding dual transform, which is injective, explicit inversion formulas are obtained both in the symmetric case and in full generality. The main tools are the Funk transform on the sphere, the Radon-John [Formula: see text]-plane transform in [Formula: see text], the Grassmannian modification of the Kelvin transform, and the Erdélyi–Kober fractional integrals.

scholarly journals Littlewood-Paley g-function and Radon Transform on the Heisenberg Group

2018 ◽  
Vol 11 (1) ◽  
pp. 138
Author(s):  
Zheng Fang ◽  
Jianxun He
Keyword(s):  
Heisenberg Group ◽  
Radon Transform ◽  
Unitary Operator ◽  
Radon Transforms ◽  
Inversion Formulas ◽  
Poisson Integrals

In this paper, we consider Radon transform on the Heisenberg group $\textbf{H}^{n}$, and obtain new inversion formulas via dual Radon transforms and Poisson integrals. We prove that the Radon transform is a unitary operator from Sobelov space $W$ into $L^{2}(\textbf{H}^{n})$. Moreover, we use the Radon transform to define the Littlewood-Paley $g$-function on a hyperplane and obtain the Littlewood-Paley theory.

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