ISSN:
1572-9206
Keywords:
sampling theorem
;
Cauchy's integral formula
;
Poisson's summation formula
;
Fourier analysis
;
complex analysis
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract First we show that several fundamental results on functions from theBernstein spaces $$B_\sigma ^p $$ (such as Bernstein's inequality andthe reproducing formula) can be deduced from a weak form of the classicalsampling theorem. In §3 we discuss the mutual equivalence of thesampling theorem, the derivative sampling theorem and a harmonic functionsampling theorem. In §§4–6 we discuss connections between thesampling theorem and various important results in complex analysis andFourier analysis. Our considerations include Cauchy's integral formula,Poisson's summation formula, a Gaussian integral, certain properties ofweighted Hermite polynomials, Plancherel's theorem, the maximum modulusprinciple, and the Phragmén–Lindelöf principle.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1010164717587
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