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The Sampling Theorem and Several Equivalent Results in Analysis (2000)

Higgins, J. R. ; Schmeisser, G. ; Voss, J. J.

Springer

Journal of computational analysis and applications 2 (2000), S. 333-371

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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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Spin density distribution in dialkyl oxalate radical anionsESR Studies on Carboxylic Esters, Part 9. For Part 8, see Ref. 1. (1988)

Brix, P. ; Helling, D. ; Voss, J.

Chichester : Wiley-Blackwell

Organic Magnetic Resonance 26 (1988), S. 324-326

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ISSN: 0749-1581

Keywords: Dialkyl oxaltes ; Radical anions ; Isotropic ESR ; Anisotropic ESR ; 2H-, 13C-, 17O-Labelling ; MO calculations ; Spin densities ; E/Z Isomers ; Chemistry ; Analytical Chemistry and Spectroscopy

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Notes: The isotropic and anisotropic ESR spectra of dialkyl oxalate radical anions, including derivatives which were labelled with 13C or 17O in the carbonyl and 2H or 13C in the alkyl groups, were measured. The spin density distribution as determined from the experimental nuclear hyperfine coupling constants agrees very well with MNDO-CI calculations. As a consequence of the strictly planar structure of the radical anions, E/Z isomers are observed.

Additional Material: 2 Ill.