Computational Methods and Function Theory 6 (2006), No. 2, 459--469
Copyright Heldermann Verlag 2006
Lev S. Maergoiz
maergoiz@krsk.info , Krasnoyarsk State Academy of Architecture and Civil Engineering, Pr. Svobodny, 82, Krasnoyarsk, 660041, Russia.
We obtain an analogue of the well-known Paley-Wiener Theorem on integral representation of entire functions of exponential type at most σ, &sigma>0, which belong to the space L2(R). We choose 1<p<2 and &sigma>0 and work in Lp(R). We find optimal estimates of the modulus on any line parallel to R, and present applications to best analytic continuation from a finite set in C for entire functions of this class. The main result was announced in [7].
Keywords: Entire functions of exponential type, integral representation, optimal estimates, Fourier transform, Fourier series, extrapolation from a finite set.
MSC 2000: 30D15.
[FullText-pdf (292 K)] [FullText-ps (480 K)]