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Generalized Bargmann transform and a group representation

✍ Scribed by R. Radha; D. Venku Naidu

Publisher
Elsevier Science
Year
2011
Tongue
French
Weight
123 KB
Volume
135
Category
Article
ISSN
0007-4497

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✦ Synopsis

Let F A (C n ) denote the Fock space associated with a real linear transformation A on C n which is symmetric and positive definite relative to the real inner product Re z, w , z, w ∈ C n . Let B A denote the Bargmann transform, mapping L 2 (R n ) unitarily onto F A (C n ). In this note, we show that one can find a group G, whose unitary irreducible representation at its base vector coincides with B * A K w up to a constant multiple, where B * A denotes the adjoint of B A and K w denotes the reproducing kernel of F A (C n ).

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