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Next seminar:
Next seminar:
28/10/2026 - Danylo Radchenko - 5:30 p. m.
28/10/2026 - Danylo Radchenko - 5:30 p. m.
(IHES, CNRS)
(IHES, CNRS)
The Hörmander-Bernhardsson extremal function
The Hörmander-Bernhardsson extremal function
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Abstract. There exists a unique minimizer of the L^1-norm among entire functions of exponential type pi satisfying f(0)=1. In 1993 Hörmander and Bernhardsson investigated the properties of this function, proving that all of its zeros are real and simple and finding a remarkably accurate approximation of its L^1-norm. However, they were unable to identify the extremal function explicitly, despite having what they believed to be a very strong numerical approximation of its Fourier transform. In this talk I will give a comprehensive description of this function, which possesses a surprising dual characterization via both differential and functional equations, among other remarkable properties.
This series of seminars is addressed to an audience interested in Harmonic Analysis in the broadest possible sense. The seminars will not necessarily concern the latest research results; the speaker may also give a talk about open problems or a survey colloquium.
The conferences take place generally every two weeks on Wednesday at 5:30 p. m. (Rome time).
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Organizers:
Tommaso Bruno (Università di Genova)
Valentina Casarino (Università degli Studi di Padova)
Bianca Gariboldi (Università Unipegaso)
Alessio Martini (Politecnico di Torino)
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