20. Mai 2026
Joachim Toft (University of Växjö)
Periodic ultra-distributions and periodic elements in modulation spaces
In the present talk we characterize periodic elements in Gevrey classes,
Gelfand-Shilov distribution spaces and modulation spaces, in
terms of estimates of involved Fourier coefficients, and by estimates of
their short-time Fourier transforms. We show that such spaces can be
completely characterised in terms of formal Fourier series with suitable
estimates on their coefficients. For periodic Gelfand-Shilov distributions
such characterisations can be found in the literature in the case when
the Gevrey parameter is strictly larger than 1. Our analysis is valid
for all positive Gevrey parameters.
As a consequence, inverse problems for diffusion equations
and similar equations on certain bounded domains can be handled.
The proofs are based on new types of formulae of
independent interests, which involve short-time Fourier transforms.
The talk is based on a joint work with E. Nabizadeh