The principal ideas of harmonic analysis on a locally compact group G which is not necessarily compact or commutative were developed in the 1940s and early 1950s. In this theory, the role of the classical fundamental harmonics is played by the irreducible unitary representations of G. The set of all equivalence classes of such representations is denoted by Ĝ and is called the dual object of G o...

This paper proposes a scheme of combining low-density parity check (LDPC) code with unitary space time modulation (USTM) for noncoherent multiple-input-multiple-output (MIMO) transmitter and receiver over Rayleigh block fading and additive white Gaussian noise (AWGN) channel. The main aim is to design the low complexity coded noncoherent MIMO receiver which is completely dependent on the struct...

In this paper, we construct explicit eigenfunctions of the local Weil representation on unitary group of one variable in the p-adic case where p is odd. The idea is to use the lattice model, and the results will be used to compute special values of certain Hecke L-functions in separated papers. We also recover Moen’s results on when a local theta lifting from U(1) to itself does not vanish. 0. ...

Let F be a local non-archimedian field and G be a split reductive group over F whose derived group is simply connected. Set G = G(F ). Let also ψ : F → C be a non-trivial additive unitary character of F . For two parabolic subgroups P and Q in G with the same Levi component M we construct an explicit unitary isomorphism FP,Q,ψ : L (G/[P, P ])→̃L(G/[Q,Q]) commuting with the natural actions of the...

In this paper we deal with a definition of Lp-Fourier transform on locally compact groups. Recall that, for locally compact abelian groups, the Hausdorff-Young inequality reads: Let 1 < p < 2 and q = p/(p − 1). If g ∈ L1(G) ∩ Lp(G), then ĝ ∈ Lq(Ĝ), with ‖ĝ‖q ≤ ‖g‖p. The inequality allows to extend the Fourier transform to a continuous operator Fp : Lp → Lq by continuity. It was generalized to t...

We consider the following class of unitary representations π of some (real) Lie group G which has a matched pair of symmetries described as follows: (i) Suppose G has a period-2 automorphism τ , and that the Hilbert space H(π) carries a unitary operator J such that Jπ = (π ◦ τ)J (i.e., selfsimilarity). (ii) An added symmetry is implied if H(π) further contains a closed subspace K0 having a cert...

We attempt to reconstruct the irreducible unitary representations of the Banach Lie group U 0 (H) of all unitary operators U on a separable Hilbert space H for which U ? I is compact, originally found by Kirillov and Ol'shanskii, through constrained quantization of its coadjoint orbits. For this purpose the coadjoint orbits are realized as Marsden-Weinstein quotients. The unconstrained system, ...

Some stimuli are perceived as unitary patterns, and others as dual or plural patterns. Such 'unity-and-variety' phenomena are explained by various process approaches of perception, such as the global precedence hypothesis, the preattentive orientation detection assumption, and the recognition-by-components model. However, these three approaches, which will be discussed in this paper, each expla...