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Page 2667 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
Siegen) Two ways to incorporate scale in the Heisenberg group with an intertwining operator.  ...  The authors construct two new wavelet-type transforms connected with the Heisenberg group H, which may be useful in signal analysis [cf. J. Segman and Y. Y. Zeevi, J. Math.  ... 

The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties

Chen Sagiv, Nir A. Sochen, Yehoshua Y. Zeevi
2006 Journal of Mathematical Imaging and Vision  
A general theorem which associates an uncertainty principle with a pair of self-adjoint operators is used in finding the minimizers of the uncertainty related to various groups.  ...  The uncertainty principle is also extended to the Affine-Weyl-Heisenberg group in one dimension.  ...  Segman and Schempp [30] introduced ways to incorporate scale in the Heisenberg group with an intertwining operator and presented the resulting signal representations.  ... 
doi:10.1007/s10851-006-8301-4 fatcat:b2rxm6ry2rebjhl3p36kumlqxy

Cross-Toeplitz Operators on the Fock–Segal–Bargmann Spaces and Two-Sided Convolutions on the Heisenberg Group [article]

Vladimir V. Kisil
2022 arXiv   pre-print
It is natural to consider these operators in the framework of representation theory of the Heisenberg group.  ...  In turn, two-sided convolutions are reduced to usual (one-sided) convolutions on the Heisenberg group of the doubled dimensionality.  ...  Acknowledgments I am grateful to Prof. N.L. Vasilevski for the suggestion two-sided convolutions as a research topic. Prof.  ... 
arXiv:2108.13710v2 fatcat:6u4ufhjdubdhpnwwimnfgdnhda

Page 5530 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
Zeevi, Image analy- sis by wavelet-type transforms: group-theoretic approach (51-77); Joseph Segman and Walter Schempp, Two ways to incorporate scale in the Heisenberg group with an intertwining operator  ...  Instead, as is shown in another paper of ours [“Two-way com- munication complexity of sum-type functions for one processor to be informed”, IEEE Trans. Inform.  ... 

Local currents for a deformed algebra of quantum mechanics with a fundamental length scale

Gerald A Goldin, Sarben Sarkar
2006 Journal of Physics A: Mathematical and General  
The relation of the irreducible representations of the deformed algebra to those of the (limiting) Heisenberg algebra is discussed, and we construct the generalized harmonic oscillator Hamiltonian in this  ...  To obtain local currents for this algebra, we extend the usual nonrelativistic local current algebra of vector fields and the corresponding group of diffeomorphisms, modeling the quantum configuration  ...  These local currents incorporate the intuitive idea of local flows in the two coordinate directions.  ... 
doi:10.1088/0305-4470/39/11/012 fatcat:deistqj7gfa5rfngknbnl7lulm

Irreducible self-adjoint representations of quantum Teichmüller space and the phase constants [article]

Hyun Kyu Kim
2020 arXiv   pre-print
Quantization of the Teichmüller space of a non-compact Riemann surface has emerged in 1980's as an approach to three dimensional quantum gravity.  ...  Upon a change of triangulations, one must construct a unitary operator between the Hilbert spaces intertwining the quantum coordinate operators and satisfying the composition identities up to multiplicative  ...  A real vector space V with a skew-symmetric bilinear form B 5 2.2. The Schrödinger representation of the Heisenberg group N , associated to an essential Lagrangian 6 2.3.  ... 
arXiv:2001.06802v2 fatcat:t5dnnxch5vdw3dfkyn42exc36m


2005 International Journal of Modern Physics D  
It carries three additional parameters: a length scale pertaining to the Planck/unification scale, a second length scale associated with cosmos, and a new dimensionless constant.  ...  Chryssomalakos and Okon, through a uniqueness analysis, have strengthened the Vilela Mendes suggestion that the immunity to infinitesimal perturbations in the structure constants of a physically-relevant  ...  related to Ref. 9 .  ... 
doi:10.1142/s0218271805008030 fatcat:posoegijurhmpacflnez5e2fgm

A cornucopia of isospectral pairs of metrics on spheres with different local geometries [article]

Z. I. Szabo
2003 arXiv   pre-print
These investigations incorporate 4 different cases since these balls and spheres are considered both on 2-step nilpotent Lie groups and on their solvable extensions.  ...  In [Sz5] the considerations are completely concluded in the ball-case and in the nilpotent-case. The other cases were mostly outlined.  ...  These Hopf hulls are intersections of ∂D by the total-geodesic scaled Heisenberg groups T X .  ... 
arXiv:math/0011034v2 fatcat:a3km22k2rvappgkpacndbsbhum

Transvectants, Modular Forms, and the Heisenberg Algebra

Peter J. Olver, Jan A. Sanders
2000 Advances in Applied Mathematics  
We discuss the amazing interconnections between normal form theory, classical invariant theory and transvectants, modular forms and Rankin-Cohen brackets, representations of the Heisenberg algebra, differential  ...  invariants, solitons, Hirota operators, star products and Moyal brackets, and coherent states.  ...  ACKNOWLEDGMENTS Thanks to Patrick Solé for correspondence on the connections between transvectants and Rankin-Cohen brackets and to Jing Ping Wang for comments.  ... 
doi:10.1006/aama.2000.0700 fatcat:ywok2zl2cnb3tpappqtc2ybwqq

A cornucopia of isospectral pairs of metrics on spheres with different local geometries

Zoltán Szabó
2005 Annals of Mathematics  
By this representation she gets an enlarged bundle with the base space v = R k and with the total space R k+2l such that the torus is nonfreely acting on the total space.  ...  These investigations incorporate four different cases since these balls and spheres are considered both on 2-step nilpotent Lie groups and on their solvable extensions.  ...  These Hopf hulls are intersections of ∂D by the total -geodesic scaled Heisenberg groups T X .  ... 
doi:10.4007/annals.2005.161.343 fatcat:ane527gr7ng7tgw3bcw77zg6ga

Ding–Iohara–Miki symmetry of network matrix models

A. Mironov, A. Morozov, Y. Zenkevich
2016 Physics Letters B  
Exhaustive for these purposes should be the Pagoda triple-affine elliptic DIM, which corresponds to networks associated with 6d gauge theories with adjoint matter (double elliptic systems).  ...  Ward identities in the most general "network matrix model" can be described in terms of the Ding-Iohara-Miki algebras (DIM).  ...  Acknowledgements We are grateful to Prof. H. Kanno for remarkable hospitality at Nagoya University at the last stage of this project. We are deeply indebted to H. Awata, H. Kanno, Y. Ohkubo and V.  ... 
doi:10.1016/j.physletb.2016.09.033 fatcat:ns7uwqozmvhjbpu5akamr6lj6m

Explicit examples of DIM constraints for network matrix models

Hidetoshi Awata, Hiroaki Kanno, Takuya Matsumoto, Andrei Mironov, Alexei Morozov, Andrey Morozov, Yusuke Ohkubo, Yegor Zenkevich
2016 Journal of High Energy Physics  
Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki  ...  Then, the Ward identities (known under the names of Virasoro/W-constraints or loop equations or regularity condition for qq-characters) are also promoted to the DIM level, where they all become corollaries  ...  The way out is to introduce a special intertwining operator with the property m|Ĉ{p}â −n = p n · m|Ĉ{p} (2.17) This allows us to rewrite (2.6) as C{p} = exp χ [m r ] { √ 2p n } = m − r Ĉ {p}Q r m + r  ... 
doi:10.1007/jhep07(2016)103 fatcat:m5cjuuqtqvf5rpm3u2g54nyjcy

The Wigner Function for General Lie Groups and the Wavelet Transform

S.T. Ali, N.M. Atakishiyev, S.M. Chumakov, K.B. Wolf
2000 Annales de l'Institute Henri Poincare. Physique theorique  
The phase spaces are coadjoint orbits in the dual of the Lie algebra of these groups and they come equipped with natural symplectic structures and Liouville-type invariant measures.  ...  We build Wigner maps, functions and operators on general phase spaces arising from a class of Lie groups, including non-unimodular groups (such as the affine group).  ...  One of us (STA) would like to acknowledge grants from the NSERC, Canada and FCAR, Québec, and the hospitality of the Centro Internacional de Ciencias, Cuernavaca.  ... 
doi:10.1007/pl00001012 fatcat:da7cqupmbza6doizfzypopi4by

The multivalued free-field maps of Liouville and Toda gravities

A. Anderson, B.E.W. Nilsson, C.N. Pope, K.S. Stelle
1994 Nuclear Physics B  
Liouville and Toda gravity theories with non-vanishing interaction potentials have spectra obtained by dividing the free-field spectra for these cases by the Weyl group of the corresponding A 1 or A 2  ...  We study the canonical transformations between interacting and free fields using the technique of intertwining operators, giving explicit constructions for the wavefunetions and showing that they are invariant  ...  For hospitality during the course of the work, C.N.P. would like to thank Chalmers University (Gothenburg), Imperial College (London) and SISSA (Trieste); K.S.S. would like to thank Chalmers University  ... 
doi:10.1016/0550-3213(94)90652-1 fatcat:ftfbxznyrvdndhqbwpmbaczr54

An Algebraic Approach to Fourier Transformation [article]

Markus Rosenkranz, Günter Landsmann
2021 arXiv   pre-print
We build the algebraic structures on the basis of a given Heisenberg group (in the general sense of nilquadratic groups enjoying a splitting property); this includes in particular the whole gamut of Pontryagin  ...  The notion of Fourier transformation is described from an algebraic perspective that lends itself to applications in Symbolic Computation.  ...  Acknowledgments We are very grateful to Heinrich Rolletschek for his helpful and friendly advice on number-theoretic issues.  ... 
arXiv:2009.12198v3 fatcat:n6ajo4at55eaxep6g5la6o5bei
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