On some Rajchman measures and equivalent Salem’s problem. (English) Zbl 1277.33004

Yakubovich, Semyon

Commun. Math. Anal. 14, No. 1, 28-41 (2013).

Summary: We construct certain Rajchman measures by using integrability properties of the Fourier and Fourier-Stieltjes transforms. In particular, we state a problem and prove that it is equivalent to the known and still unsolved question posed by R. Salem [Trans. Am. Math. Soc. 53, 427–439 (1943; Zbl 0060.13709)] whether Fourier-Stieltjes coefficients of the Minkowski question mark function vanish at infinity.

MSC:

33C10	Bessel and Airy functions, cylinder functions, \({}_0F_1\)
42A16	Fourier coefficients, Fourier series of functions with special properties, special Fourier series
42B10	Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
44A15	Special integral transforms (Legendre, Hilbert, etc.)

Keywords:

fractional Laplacian; Green function; symmetric stable process; Dirichlet problem

Citations:

Zbl 0060.13709

References:

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