Fundamental to the theory of joint signal representations is the idea of associating a variable, such as time or frequency, with an operator, a concept borrowed from quantum mechanics. Each variable can be associated with a Hermitian operator, or equivalently and consistently, as we show, with a parame-terized unitary operator. It is well-known that the eigenfunctions of the unitary operator de...

In this paper, the unitary dual of p-adic group SO(7) with support on minimal parabolic subgroup is determined. explicit determination external approach used, which represents basic for finding dual, and consists two main steps: a complete description non-unitary extraction classes unitarizable representations among obtained irreducible subquotients. We expect that our results will provide deep...

There is almost unanimous consensus among the theorists of consciousness that the phenomenal character of a mental state cannot exist without consciousness. We argue for a reappraisal of this consensus. We distinguish two models of phenomenal consciousness: unitary and dual. Unitary model takes the production of a phenomenal quality and it's becoming conscious to be one and the same thing. The ...

We locate a family of small unitary representations of the orthogonal groups in the theta correspondence for the dual pairs `

1 Euler Characteristics and Infinitesimal Characters 4 1.1 The unitary duals of SL2(R) and SL4(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Euler characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Euler-Poincaré functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Euler characteristics in t...

The duality principle for Gabor frames states that a Gabor sequence obtained by a time-frequency lattice is a frame for L(R ) if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality principle extends to any dual pairs of projective unitary representations of countable groups. We examine the existence problem of dual pairs and establish some connectio...