Some remarks on the Cauchy Problem for Schr\"odinger type equations in Gelfand-Shilov spaces
Abstract
We consider the Cauchy problem for Schr\"odinger type operators. Under a suitable decay assumption on the imaginary part of the first order coefficients we prove well-posedness of the Cauchy problem in Gelfand-Shilov classes. We also discuss the optimality of our result through some examples.
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