132 INDEX
Laplace–Beltrami operator, 2, 28
light cone, 11
Mehler kernel, 19
Meijer’s G-distribution, 89
Meijer’s G-function, 22, 23, 115
Meijer’s G-transform, 24
Mellin transform, 81
—, of Bessel function, 110
Mellin–Barnes type integral, 90, 94, 115
metaplectic group, 15
minimal representation, 2, 13, 16, 31
Minkowski space, 19
obius transform, 17
modified Bessel function
—, of the first kind, 107
—, of the third kind, 108
multiplicity free, 21
multiplicity-free decomposition, 81
N-picture, 17, 27, 120
oscillator representation, 15
Parseval type formula, 21
Plancherel formula
—, for Meijer’s G-transform, 24
—, FC , 18, 78
—, G-function, 61
Radon transform, 8, 79, 81
reciprocal formula, 18
—, for Meijer’s G-transform, 24
—, FC , 18, 78
—, G-function, 61
Riesz distribution, 105
Riesz potential, 82
Schr¨ odinger, 78
Schr¨ odinger model, 2, 15–17, 33, 120
Schwartz space, 6
Segal–Shale–Weil representation, 15
Siegel parabolic subgroup, 15
smooth vector, 7, 35
solution model, 20
spherical harmonics, 23, 113
spherical representation, 16
symplectic group, 15
symplectic Lie algebra, 9
tempered distribution, 17, 19, 63
theta correspondence, 16, 31
ultra-hyperbolic equation, 8, 16
uncertainty relation, 20
unitary inversion operator, 8, 20, 46, 77
wave front set, 14
Weil representation, 3, 9, 15, 33, 60, 78
Weyl algebra, 4, 37
Yamabe operator, 17, 28
Y -Bessel function, 108
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