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A note on generalized Weyl-Heisenberg frames

S. Dahlke
1994 Applied Mathematics Letters  
In this note, the concept of Weyl-Heisenberg frames is generalized to some specific locally compact groups. An existence theorem based on certain subgroups is proved.  ...  A discrete subgroup that yields a compact quotient space is sometimes called a un$~m lattice. Such a uniform lattice often exists, see [8] for details.  ...  Therefore, we define a generalized Weyl-Heisenberg frame for L2(G, dmG) by means of these unitary representations and the action of another discrete set H c G, i.e., we say that 4 generates a Weyl-Heisenberg  ... 
doi:10.1016/0893-9659(94)90117-1 fatcat:ot3wtl2hrjchtac5dw34xdbjk4

On sufficient density conditions for lattice orbits of relative discrete series [article]

Ulrik Enstad, Jordy Timo van Velthoven
2021 arXiv   pre-print
This note provides new criteria on a unimodular group G and a discrete series representation (π, ℋ_π) of formal degree d_π > 0 under which any lattice Γ≤ G with vol(G/Γ) d_π≤ 1 (resp. vol(G/Γ) d_π≥ 1)  ...  admits g ∈ℋ_π such that π(Γ) g is a frame (resp.  ...  Acknowledgements U.E. gratefully acknowledges support from the The Research Council of Norway through project 314048.  ... 
arXiv:2112.05502v1 fatcat:y25b74hb7zdo3p4yoa5zqmfkw4

Page 3447 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
The lattice L is then recovered as a set of continuous order-preserving maps from its dual space into the 2- element chain, discretely topologised.  ...  Comer (1-CITA; Charleston, SC) 97f:06014 06B15 06B10 PloStica, Miroslav (SK-AOS2; KoSice) A natural representation of bounded lattices.  ... 

Discrete Weyl–Heisenberg transforms

J. Zak
1996 Journal of Mathematical Physics  
Phys. 47, 063501 (2006) Quaternionic root systems and subgroups of the Aut(F4) J. Math. Phys. 47, 043507 (2006) A note on monopole moduli spaces J. Math.  ...  The concepts of von Neumann lattices and tight frames are used for defining discrete quantum mechanical transforms in the phase plane.  ...  Also in this approximation the frame operator FhN'=N gives the number of the WH set states in a unit cell of the VNG lattice.  ... 
doi:10.1063/1.531603 fatcat:le5w7dfzgfa65ixyqfpapy6pgu

Page 522 of American Society of Civil Engineers. Collected Journals Vol. 119, Issue 2 [page]

1993 American Society of Civil Engineers. Collected Journals  
By utilizing the repetitive pattern of these lattice structures, con- tinuum representations can yield finite-element models that have signifi- cantly fewer degrees of freedom than those generated using  ...  The idea of using continuum models to approximate the response of a discrete model existed before computers were invented.  ... 


Timor Melamed
2011 Electromagnetic Waves  
The propagating field is described as a discrete superposition of tilted, shifted and delayed electromagnetic pulsed-beam waveobjects over the frame spectral lattice.  ...  The present contribution is concerned with an exact frame-based pulsed-beams expansion of planar aperture timedependent electromagnetic fields.  ...  Discrete frame spectral lattice.  ... 
doi:10.2528/pier11012001 fatcat:yyfev52nszbzzoqp4fazgro5uy

Dual Gabor frames: theory and computational aspects

T. Werther, Y.C. Eldar, N.K. Subbanna
2005 IEEE Transactions on Signal Processing  
Therefore, all results in Gabor analysis that are based on the positivity of the frame operator cannot be applied directly.  ...  The advantage of the proposed characterization is that the algebraic system for computing the Gabor dual elements preserves the high structure of usual Gabor frames, leading to computationally efficient  ...  The first author would like also to thank the people from the department of electrical engineering of the Technion for their great hospitality and support during his stay in Haifa.  ... 
doi:10.1109/tsp.2005.857049 fatcat:24ouyedrirhdnmnwwudlmmlcw4

A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers

Paul Benioff
2009 Advances in Mathematical Physics  
As physical systems in each frame the strings have a discrete Schrodinger dynamics on the lattices.  ...  A discussion of parent frame images includes the proposal that points of stagejframe lattices have images as hybrid systems in parent frames.  ...  Space and Time Lattices in Reference Frames A first step in this direction is to expand the domain of each frame in the field to include discrete lattices of space and time.  ... 
doi:10.1155/2009/452738 fatcat:apktjzev5neorivo4nbfenwnau

The density theorem for discrete series representations restricted to lattices [article]

José Luis Romero, Jordy Timo van Velthoven
2021 arXiv   pre-print
This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume.  ...  The focus is on the density theorem, which provides a trichotomy characterizing the existence of cyclic vectors and separating vectors, and frames and Riesz sequences.  ...  Let Γ ⊆ G be a lattice and let (π, H π ) be a discrete series σrepresentation of G of formal dimension d π > 0.  ... 
arXiv:2003.08347v3 fatcat:wuy6djhslvcexm3jb5ax23gsr4

Frames in rotated time-frequency planes

A. Bultan, A.N. Akansu
1999 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)  
Weyl-Heisenberg frames are complete signal representations corresponding to rectangular tiling of the time-frequency plane.  ...  Extensions of these frames are obtained in the rotated time-frequency planes by using the fractional Fourier transformation. It is shown that rotation does not affect the frame bounds.  ...  Using the unitary property of the FRFT, it is shown that rotation does not change the frame bounds. At some discrete angles, a lattice mapping from rotated to Cartesian coordinates is obtained.  ... 
doi:10.1109/icassp.1999.756231 dblp:conf/icassp/BultanA99 fatcat:5n2lptvcfbaa3mftabq7bhbjr4

Coupling non-gravitational fields with simplicial spacetimes

Jonathan R McDonald, Warner A Miller
2010 Classical and quantum gravity  
The inclusion of source terms in discrete gravity is a long-standing problem.  ...  RC provides a particularly insightful approach to this problem with its purely geometric representation of spacetime.  ...  One of us (JRM) would also like to acknowledge partial support from NSF grant 0638662 and DFG grant SFB/TR7 "Gravitational Wave Astronomy".  ... 
doi:10.1088/0264-9381/27/9/095011 fatcat:vazkyhjkuzg67d5aslyekhwr3m

A pulsed beam summation formulation for short pulse radiation based on windowed Radon transform (WRT) frames

A. Shlivinski, E. Heyman, A. Boag
2005 IEEE Transactions on Antennas and Propagation  
We introduce a novel formulation for short pulse radiation from an expanded aperture distribution, wherein the field is expanded, directly in the time-domain (TD) into a discrete lattice of shifted, tilted  ...  The formulation is based on a new class of frames, termed WRT frames.  ...  Figure 1 : 1 (a) The PB summation representation of (5). (b) The discrete W-SST (or WRT) illustrated in the space-time data domain u 0 (x, t).  ... 
doi:10.1109/tap.2005.854550 fatcat:krr3moaqlrgxnm5gqvc2sw7axa

Coherent systems over approximate lattices in amenable groups [article]

Ulrik Enstad, Jordy Timo van Velthoven
2022 arXiv   pre-print
For a projective discrete series representation (π, ℋ_π) of G of formal degree d_π > 0, we show that D^-(Λ) ≥ d_π / k is necessary for the coherent system π(Λ) g to be complete in ℋ_π.  ...  Let G be a second-countable amenable group with a uniform k-approximate lattice Λ.  ...  Acknowledgements U.E. gratefully acknowledges support from the The Research Council of Norway through project 314048.  ... 
arXiv:2208.05896v1 fatcat:rldmhuujw5bv5kwwlpxumkdpjy

Asymptotic Boundary Forms for Tight Gabor Frames and Lattice Localization Domains

H. G. Feichtinger, K. Nowak, M. Pap
2015 Journal of Applied Mathematics and Physics  
We consider Gabor localization operators G , φ Ω defined by two parameters, the generating function φ of a tight Gabor frame { } λ λ φ ∈Λ , indexed by a lattice 1 2  ...  Acknowledgments The authors would like to thank ESI (Erwin Schrödinger Institute, University of Vienna), where the joint work on this paper began (Thematic Programme: Modern Methods of Time-Frequency Analysis  ...  II), and CIRM (Centre international de recontres mathématique, Luminy, Marseille), where the three authors had the chance to complete their work during the period of Hans Feichtinger's Morlet Chair.  ... 
doi:10.4236/jamp.2015.310160 fatcat:kz5fgcnj55cwfjc7vt2yxpoeba

Discrete directional wavelet bases for image compression

Pier L. Dragotti, Vladan Velisavljevic, Martin Vetterli, Baltasar Beferull-Lozano, Touradj Ebrahimi, Thomas Sikora
2003 Visual Communications and Image Processing 2003  
In this paper, a new truly separable discrete multi-directional transform is proposed with a subsampling method based on lattice theory.  ...  The application of the wavelet transform in image processing is most frequently based on a separable construction.  ...  While the design of multi-directional frames is pretty straightforward, 2 the construction of multi-directional bases having good representation properties presents a more difficult challenge due to the  ... 
doi:10.1117/12.509905 fatcat:mbvexuc26jgs7a26pys2tcgcfa
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