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Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.
T. Godoy, and L. Saal. "A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)." Colloquium Mathematicae 106.2 (2006): 231-255. <http://eudml.org/doc/284345>.
@article{T2006, abstract = {Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.}, author = {T. Godoy, L. Saal}, journal = {Colloquium Mathematicae}, keywords = {Heisenberg group; spherical transform; Schwartz space}, language = {eng}, number = {2}, pages = {231-255}, title = {A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)}, url = {http://eudml.org/doc/284345}, volume = {106}, year = {2006}, }
TY - JOUR AU - T. Godoy AU - L. Saal TI - A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q) JO - Colloquium Mathematicae PY - 2006 VL - 106 IS - 2 SP - 231 EP - 255 AB - Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula. LA - eng KW - Heisenberg group; spherical transform; Schwartz space UR - http://eudml.org/doc/284345 ER -