The inverse Segal–Bargmann transform for compact Lie groups
BC Hall - journal of functional analysis, 1997 - Elsevier
journal of functional analysis, 1997•Elsevier
In this paper I give a new inversion formula (Theorem 1) for the generalized Segal–
Bargmann transform introduced in BC Hall, J. Funct. Anal. 122 (1994), 103–151. The
inversion formula may be viewed as a formula for theinverseheat operator for a compact Lie
group. I then use this formula to give a new direct proof of the unitary of theK-invariant form
of the Segal–Bargmann transform (Theorem 2). The proof of the inversion formula relies on
an identity (Theorem 5) which relates the Laplacian for a compact Lie groupKto the …
Bargmann transform introduced in BC Hall, J. Funct. Anal. 122 (1994), 103–151. The
inversion formula may be viewed as a formula for theinverseheat operator for a compact Lie
group. I then use this formula to give a new direct proof of the unitary of theK-invariant form
of the Segal–Bargmann transform (Theorem 2). The proof of the inversion formula relies on
an identity (Theorem 5) which relates the Laplacian for a compact Lie groupKto the …
In this paper I give a new inversion formula (Theorem 1) for the generalized Segal–Bargmann transform introduced in B. C. Hall,J. Funct. Anal.122(1994), 103–151. The inversion formula may be viewed as a formula for theinverseheat operator for a compact Lie group. I then use this formula to give a new direct proof of the unitary of theK-invariant form of the Segal–Bargmann transform (Theorem 2). The proof of the inversion formula relies on an identity (Theorem 5) which relates the Laplacian for a compact Lie groupKto the Laplacian for the non-compact dual symmetric space KC /K.
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