Further, it led to the theory of microfunctions, interest in microlocal aspects of linear partial differential equations and Fourier theory such as wave fronts, and ultimately to the current developments in D-module theory.
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Poisson, Liouville, Fourier and others studied partial differential equations and harmonic analysis.
Specializing in harmonic analysis and operator theory, he is mostly known for, together with Steve Hofmann, Michael Lacey, Alan McIntosh and Philippe Tchamitchian, solving the famous Kato's conjecture.
Harald Bohr - the brother of physicist Niels Bohr - is one famous alumni of the department; his research in harmonic analysis and almost periodic functions in the 1930s laid the foundation for a huge drive in analysis.
Before Kalman, time series analysis and classical control theory studied the frequency domain, using harmonic analysis, especially Laplace and Fourier transforms.
In 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in real, complex, and harmonic analysis.
In 1999 Nazarov was awarded the Salem Prize "for his work in harmonic analysis, in particular, the uncertainty principle, and his contribution to the development of Bellman function methods".