The Bargmann transform on modulation and Gelfand–Shilov spaces, with applications to Toeplitz and pseudo-differential operators

By J. Toft. 2012

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Pseudo‐differential operators in a Gelfand–Shilov setting (2015, unknown): “2 in [20], it suffices to verify that ω2(x − y/2, ξ + η/2) ω1(x + y/2, ξ − η/2) ω(x, ξ, η, y), (4.”
Images of function and distribution spaces under the Bargmann transform (2014, methodology): “We apply these results to characterize the GelfandShilov spaces and their distribution spaces, in terms of short-time Fourier transforms and to show that all these function and distribution spaces are obtained by suitable unions or intersections of the broad family of modulation spaces, introduced i”