Abstract
Most of the “extremal problems” of Harmonic (or Fourier) Analysis which emerged before the year 2000 were actually born in the twentieth century, and their emergences were scattered throughout that century, including the two world war periods. A great many of these problems pertain to polynomials, trigonometric polynomials and (finite) exponential sums. Writing a reasonably complete monograph on this huge subject (even if we choose to restrict it to polynomials only) would be a monumental task, although the literature does indeed contain some valuable monographs on various aspects of the subject. The present text just touches upon a number of extremal problems on polynomials and trigonometric polynomials, with the hope of expanding this same text in the near future to a much larger version, and ultimately to a “reasonably complete” monograph (but only with the help of other mathematicians.)
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Saffari, B. (2001). Some polynomial extremal problems which emerged in the twentieth century. In: Byrnes, J.S. (eds) Twentieth Century Harmonic Analysis — A Celebration. NATO Science Series, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0662-0_11
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