Joachim Toft: Periodic ultra-distributions and periodic elements in modulation spaces

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Joachim Toft


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 coeffi- cients, 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 interestswhen evaluating the Fourier coefficients and which involve short-time Fourier transforms.

The talk is based on a joint work with E. Nabizadeh.


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