Geodesic
Asymptotics of Fourier and Laplace transforms in weighted spaces of analytic functions
Algebra i analiz, Tome 14 (2002) no. 4, pp. 107-140.

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We study the asymptotics of the Fourier transform in weighted Hardy spaces of analytic functions in the upper half-plane, and of the Laplace transform in weighted spaces of entire functions of zero exponential type. The results are applied to two closely related problems posed by Dyn'kin: we find the asyniptotics of the depth of zero for flat functions in non-quasianalytic Denjoy–Carleman classes, and of the exact majorant in a version of the Carleman–Levinson–Sjöberg $\log$-$\log$-theorem.
Keywords: Flat non-quasianalytic functions, the $\log$-$\log$-theorem, asymptotics of the Fourier and Laplace transform. 
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     author = {V. Matsaev and M. Sodin},
     title = {Asymptotics of {Fourier} and {Laplace} transforms in weighted spaces of analytic functions},
     journal = {Algebra i analiz},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2002_14_4_a6/}
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V. Matsaev; M. Sodin. Asymptotics of Fourier and Laplace transforms in weighted spaces of analytic functions. Algebra i analiz, Tome 14 (2002) no. 4, pp. 107-140. http://geodesic.mathdoc.fr/item/AA_2002_14_4_a6/