Splitting entire functions with zeros in a strip. (English. Russian original) Zbl 0865.46029

Yulmukhametov, R. S.

Sb. Math. 186, No. 7, 1071-1084 (1995); translation from Mat. Sb. 186, No. 7, 147-160 (1995).

Summary: The following result is proved. If \(\varphi\) is a smooth function with support in the interval \([-N,N]\) and if all the zeros of its Fourier transform \[ \widehat{\varphi}(\lambda)=\int e^{i\lambda t}\varphi(t)dt \] are in some horizontal strip, then \(\varphi\) can be represented as a convolution of two smooth functions with supports in the interval \([-N/2,N/2]\).

MSC:

46F12	Integral transforms in distribution spaces
30D20	Entire functions of one complex variable (general theory)
42A85	Convolution, factorization for one variable harmonic analysis

Keywords:

Fourier transform; convolution of two smooth functions