Related papers: Shift-invariant spaces on SI/Z Lie groups

In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…

By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterised by its invariants must be of aligned type II; i.e., there exists a frame such that all the curvature tensors are simultaneously of…

We discuss a fine tuning of the co- and contra-variant transforms through construction of specific fiducial and reconstructing vectors. The technique is illustrated on three different forms of induced representations of the Heisenberg…

We study Beurling-Fourier algebras of $ q $-deformations of compact semisimple Lie groups. In particular, we show that the space of irreducible representations of the function algebras of their Drinfeld doubles is exhausted by the…

We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application we study the `internalized' automorphism group of a…

We study the existence of certain characteristically nilpotent Lie algebras with flat coadjoint orbits. Their connected, simply connected Lie groups admit square-integrable representations modulo the center. There are many examples of…

Using techniques of deformation (bi)quantization we establish a non-canonical algebra isomorphism between the deformed reduction algebra and the invariant differential operators on G/H. Further results concerning other deformations of these…

We defined a non-commutative algebra representation for quantum systems whose phase space is the cotangent bundle of the Lorentz group, and the non-commutative Fourier transform ensuring the unitary equivalence with the standard group…

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…

The group E(3)=SO(3) *s T(3), that is the homogeneous subgroup of the Galilei group parameterized by rotation angles and velocities, defines the continuous group of transformations between the frames of inertial particles in Newtonian…

We study the Lie algebras of the covariant representations transforming the matter fields under the de Sitter isometries. We point out that the Casimir operators of these representations can be written in closed forms and we deduce how…

Using the notions of frame transform and of square integrable projective representation of a locally compact group $G$, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier…

Let G be the group of points of a split reductive algebraic group over a local field k and let X=G/U where U is a maximal unipotent subgroup of G. In this paper we construct certain canonical G-invariant space S(X) (called the Schwartz…

Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only…

For a symmetric $R$-space $K/L=G/P$ the standard intertwining operators provide a canonical $G$-invariant pairing between sections of line bundles over $G/P$ and its opposite $G/\overline{P}$. Twisting this pairing with an involution of $G$…

In this article we obtain families of frames for the space B_\omega of functions with band in [-\omega,\omega] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant,…

This paper constructs translation invariant operators on L2(R^d), which are Lipschitz continuous to the action of diffeomorphisms. A scattering propagator is a path ordered product of non-linear and non-commuting operators, each of which…

We consider Lie groups equipped with a left-invariant cyclic Lorentzian metric. As in the Riemannian case, in terms of homogeneous structures, such metrics can be considered as different as possible from bi-invariant metrics. We show that…

This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…

We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.