IISER Mohali, Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306


Prof. Joachim Toft (Linnaeus University, Sweden)

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In the present talk we haracterize 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 dffiusion equations and similar equations on certain bounded domains can be handled.
The proofs are based on new types of formulae of independent interests when evaluating the Fourier coefficients and which involve short-time Fourier transforms.The talk is based on a joint work with E. Nabizadeh.

[1] M. Reich Superposition in Modulation Spaces with Ultradierentiable Weights, (preprint)arXiv:1603.08723.
[2] M. Reich, M. Reissig, W. Sickel Non-analytic Superposition Results on Modulation Spaces with Subex-ponential Weights, J. Pseudo-Dier. Oper. Appl. 7 (2016), 365{409.
[3] J. Toft Periodicity, and the Zak transform on Gelfand-Shilov and modulation spaces, Complex Analysis and Operator Theory (appeared online 2020).
[4] J. Toft, E. Nabizadeh Periodic distributions and periodic elements in modulation spaces, Adv. Math.323 (2018), 193{225.

Meeting ID: 943 7403 6747
Passcode: 518065
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