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Sergey Denisov: some math and more
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2026-01-15 23:00:39
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sdenisov | Sergey Denisov: some math and more sdenisov Sergey Denisov: some math and more Home About Some non-math topics Subscribe to feed Analog of Lusin’s conjecture for orthogonal polynomials from Szego class December 24, 2019 in Uncategorized | 1 comment The celebrated Carleson theorem for trigonometric Fourier series solved positively the Lusin’s conjecture. It says, in particular, that for every , the Fourier series converges for a.e. . This results follows from the estimate on the Carleson’s maximal function. In the preprint with R. Bessonov, we studied the analog of Lusin’s conjecture for polynomials orthogonal on the unit circle. Suppose is probability measure on . It belongs to Szego’s class if . This class plays crucial role in many branches of classical analysis and probability (see other posts). If is in Szego’s class, we can define Szego’s function by the formula Denote the polynomials orthonormal with respect to by . The analog...
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