We study three exceptional theta correspondences for p-adic groups, where one member of the dual pair is group $$G_2$$ . prove Howe duality conjecture these pairs and a dichotomy theorem, determine explicitly lifts all non-cuspidal representations.

We determine the unitary dual of the geometric graded Hecke algebras with unequal parameters which appear in Lusztig’s classification of unipotent representations for exceptional p-adic groups. The largest such algebra is of type F4. Via the Barbasch-Moy correspondence of unitarity applied to this setting, this is equivalent to the identification of the corresponding unitary unipotent represent...

We give a characterization of all (quasi) aane frames in L 2 (R n) which have a (quasi) aane dual in terms of the two simple equations in the Fourier transform domain. In particular, if the dual frame is the same as the original system, i.e. it is a tight frame, we obtain the well known characterization of wavelets. Although these equations have already been proven under some special conditions...

We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique du...

Dual systems of steel moment frame and reinforced concrete shear wall have combined the advantages of steel frames and reinforced concrete shear wall. These walls have increased the lateral stiffness of steel frames and have reduced seismic demands on steel frames thus providing opportunities to use such system. In this research intermediate dual system of steel moment frame was chosen with int...

D. Prasad showed that the sign of a self-dual representation finite or p-adic reductive group is often detected by central element. We study extension his results to some more general situations and make observations about consequences results.

We discuss an elementary procedure that allows us to construct dual pairs of wavelet frames based on certain dual pairs of Gabor frames and vice versa. The construction preserves tightness of the involved frames. Starting with Gabor frames generated by characteristic functions the construction leads to a class of tight wavelet frames that include the Shannon (orthonormal) wavelet, and applying ...