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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

2006
*
Journal of Mathematical Imaging and Vision
*

A general theorem which associates

doi:10.1007/s10851-006-8301-4
fatcat:b2rxm6ry2rebjhl3p36kumlqxy
*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. ...##
###
Cross-Toeplitz Operators on the Fock–Segal–Bargmann Spaces and Two-Sided Convolutions on the Heisenberg Group
[article]

2022
*
arXiv
*
pre-print

It is natural

arXiv:2108.13710v2
fatcat:6u4ufhjdubdhpnwwimnfgdnhda
*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. ...##
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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. ...##
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Local currents for a deformed algebra of quantum mechanics with a fundamental length scale

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. ...

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

2020
*
arXiv
*
pre-print

Quantization of

arXiv:2001.06802v2
fatcat:t5dnnxch5vdw3dfkyn42exc36m
*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. ...##
###
MINIMAL SPATIO-TEMPORAL EXTENT OF EVENTS, NEUTRINOS, AND THE COSMOLOGICAL CONSTANT PROBLEM

2005
*
International Journal of Modern Physics D
*

It carries three additional parameters: a length

doi:10.1142/s0218271805008030
fatcat:posoegijurhmpacflnez5e2fgm
*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 . ...##
###
A cornucopia of isospectral pairs of metrics on spheres with different local geometries
[article]

2003
*
arXiv
*
pre-print

These investigations

arXiv:math/0011034v2
fatcat:a3km22k2rvappgkpacndbsbhum
*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 . ...##
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Transvectants, Modular Forms, and the Heisenberg Algebra

2000
*
Advances in Applied Mathematics
*

We discuss

doi:10.1006/aama.2000.0700
fatcat:ywok2zl2cnb3tpappqtc2ybwqq
*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. ...##
###
A cornucopia of isospectral pairs of metrics on spheres with different local geometries

2005
*
Annals of Mathematics
*

By this representation she gets

doi:10.4007/annals.2005.161.343
fatcat:ane527gr7ng7tgw3bcw77zg6ga
*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 . ...##
###
Ding–Iohara–Miki symmetry of network matrix models

2016
*
Physics Letters B
*

Exhaustive for these purposes should be

doi:10.1016/j.physletb.2016.09.033
fatcat:ns7uwqozmvhjbpu5akamr6lj6m
*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. ...##
###
Explicit examples of DIM constraints for network matrix models

2016
*
Journal of High Energy Physics
*

Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories

doi:10.1007/jhep07(2016)103
fatcat:m5cjuuqtqvf5rpm3u2g54nyjcy
*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 ...##
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The Wigner Function for General Lie Groups and the Wavelet Transform

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. ...

##
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The multivalued free-field maps of Liouville and Toda gravities

1994
*
Nuclear Physics B
*

Liouville and Toda gravity theories

doi:10.1016/0550-3213(94)90652-1
fatcat:ftfbxznyrvdndhqbwpmbaczr54
*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 ...##
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An Algebraic Approach to Fourier Transformation
[article]

2021
*
arXiv
*
pre-print

We build

arXiv:2009.12198v3
fatcat:n6ajo4at55eaxep6g5la6o5bei
*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. ...
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