Mapping properties for the Bargmann transform on modulation spaces (Q1758392)

The authors investigate mapping properties for the Bargmann transform on an extended family of modulation spaces \(M(\omega, \mathcal{B})\) with weights \(\omega\) and translation invariant BF-spaces \(\mathcal{B}\). They prove that this transform is isometric and bijective from modulaton spaces \(M(\omega, \mathcal{B})\) to convenient Banach spaces \(A(\omega, \mathcal{B})\) of analytic functions. The authors use the results to establish mapping properties of Berezin-Toeplitz operators and get spectral properties of harmonic oscillators on modulation spaces.